
<PAGE>   1
                                                                   Exhibit 10.31


                           STOCK ISSUANCE AGREEMENT

        This STOCK ISSUANCE AGREEMENT is made as of June 26, 1996 among
Ameripath, Inc., a Delaware corporation (the "Company"), The First National
Bank of Boston ("FNBB"), FSC Corp., a Massachusetts corporation and an
affiliate of FNBB, NationsBank, N.A. (South) ("NationsBank") and Atlantic
Equity Corporation, a North Carolina corporation and an affiliate of
(NationsBank).

                                   RECITALS


        The Company and FNBB and NationsBank (the "Banks") are party to a
Credit Agreement dated as of May 29, 1996 as amended and as in effect on the
date hereof (the "Credit Agreement") in which the Company agreed to pay to the
Banks in accordance with their respective Percentage Interests a closing fee of
$200,000 (the "Closing Fee").

        FNBB and NationsBank are willing to assign their respective rights to
the Closing Fee to FSC Corp. and Atlantic Equity Corporation (the "Holders"),
respectively, and the Company is willing to issue and sell to such Holders as
satisfaction of the Closing Fee owed to the Banks, the number of shares of
Common Stock set forth opposite the name of the Holders on Schedule 1 hereto,
all on the terms and conditions set forth herein.

                                  AGREEMENT


        In consideration of the foregoing, and the representations, warranties,
covenants and conditions set forth below, the parties hereto, intending to be
legally bound, hereby agree as follows:

        1.  Definitions.  Capitalized terms defined in the Credit Agreement and
used but not otherwise defined in this Agreement are used herein as so defined.

        2.  Assignment.  FNBB and NationsBank hereby assign to FSC Corp. and
Atlantic Equity Corporation, respectively, and FSC Corp. and Atlantic Equity
Corporation hereby assume, all of the FNBB's and NationsBank's respective
rights to the Closing Fee.

        3.  Sale and Purchase of Subscription Securities.  On the terms and
subject to the conditions hereof, the Company hereby agrees to sell to each
Holder, and by its execution of this Agreement such Holder agrees to accept
from the Company as payment by the Company of the Closing Fee the number of
shares of Common Stock set forth opposite the name of such Holder on Schedule 1
hereto.  The shares of Common Stock being purchased by the Holders hereunder
are referred to herein as the "Securities."  The Company agrees to deliver

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certificates for the Securities to each Holder, registered in the name of such
Holder, immediately following the execution of this Agreement.

        4.  Representations and Warranties of the Company.  The Company
represents and warrants to each of the Banks and Holders that"

            4.1  Each of the Company and its Subsidiaries is duly organized and
        validly existing and in good standing under the laws of the
        jurisdiction of its incorporation, with all power and authority,
        corporate or otherwise, necessary to enter into and perform this
        Agreement and own its properties and carry on the business now conducted
        or proposed to be conducted by it.  The Company has made available to
        the Holders true and complete copies of the Company's certificate of
        incorporation and the by-laws as in effect on the date hereof.

            4.2  The Company has taken all corporate action required to
        authorize the execution and delivery of this Agreement and the issuance
        of the Securities.

            4.3  The Securities, when issued, will be duly authorized,
        validly issued, fully paid and non-assessable.

            4.4  This Agreement is a legal, valid and binding obligation of the
        Company, enforceable in accordance with terms.

        5.  Incidental ("Piggy-Back") Registration Rights.  In the event the
Company effects any registration of shares of its capital stock under the
Securities Act of 1933, as amended, for its own account or for the account of
any other Person subsequent to the initial registration by the Company of
shares of its capital stock, then the Holders shall have the right to include
the Securities in such registration if and to the extent of the most favorable
rights of any other holder of any other shares of capital stock of the Company
to include shares in such registration.  Notwithstanding the foregoing
provisions of this Section 5, in the event such registration relates to an
underwritten offering (whether or not on a firm commitment basis), if the
managing underwriter of such underwritten offering shall determine that the
shares to be included in such registration should be limited due to market
conditions or otherwise, all of the Securities shall be excluded prior to the
exclusion of any other shares not held by officers or employees of the Company
and shall be included prior to the inclusion of any shares held by officers or
employees of the Company.

        6.  Indemnities.  The Company agrees to indemnify and hold harmless
each Holder, from and against all losses, damages, liabilities and expenses
(including without limitation reasonable attorneys fees and charges) resulting
from any breach of any representation, warranty or agreement of such
indemnifying party or any misrepresentation by such indemnifying party in this
Agreement.

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7.  Restrictions on Transfer.
   
    7.1  Restrictive Legend.  All certificates representing Securities shall
bear a legend in substantially the following form:

    "THE SECURITIES REPRESENTED BY THIS CERTIFICATE WERE ISSUED IN A PRIVATE
PLACEMENT, WITHOUT REGISTRATION UNDER THE SECURITIES ACT OF 1933, AS AMENDED
(THE "ACT"), AND MAY NOT BE SOLD, ASSIGNED, PLEDGED OR OTHERWISE TRANSFERRED IN
THE ABSENCE OF AN EFFECTIVE REGISTRATION UNDER THE ACT COVERING THE TRANSFER OR
A LEGAL OPINION OF COUNSEL ACCEPTABLE TO THE ISSUER THAT REGISTRATION UNDER THE
ACT IS NOT REQUIRED."

   7.2  Termination of Restrictions.  The restrictions imposed by Section 7.1
hereof upon the transferability of Securities shall cease and terminate as to
any particular Securities when, in the written opinion of Ropes & Gray or other
counsel reasonably acceptable to the Company, which opinion shall also be
delivered and reasonably acceptable to the Company's transfer agent, (i) such
restrictions are no longer required in order to assure compliance with the
Securities Act or (ii) such Securities shall have been registered under the
Securities Act or transferred in compliance with Rule 144 thereunder.  Whenever
such restrictions shall cease and terminate as to any Securities or such
Securities shall be transferable in compliance with paragraph (k) of Rule 144,
the holder thereof shall be entitled to receive from the Issuer, without
expense, new certificates not bearing the legend set forth in Section 7.1
hereof.

8.  Miscellaneous.

    8.1  This Agreement shall be considered a Credit Document.

    8.2  This Agreement and the other agreements referred to herein set forth
the entire understanding among the parties with respect to the subject matter
thereof.

    8.3  This Agreement can be changed only by an instrument in writing signed
by the party against whom enforcement of such change is sought.

    8.4  This Agreement shall bind and inure to the benefit of the parties
hereto and their respective successors, assigns, heirs and representatives;
provided, however, that no Holder may assign any of such Holder's rights
hereunder except in connection with a transfer of the Securities in compliance
with the terms and conditions of Section 7 of this Agreement.

    8.5  All covenants, agreements, representations and warranties made herein
shall survive the execution and delivery hereof and transfer of any Securities.

                                     -3-

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   8.6.  This Agreement may be executed in any number of counterparts, each of
which shall be deemed an original but all of which shall together constitute
one and the same instrument.

   8.7.  All notices, requests, consents and demands will be in writing and will
be personally delivered, mailed, postage prepaid, telecopied or telegraphed, if
to the company to it at its address set forth in Exhibit 1.7 of the Credit
Agreement or if to the Holders as follows:

                If to FSC Corp., at
                100 Federal Street
                Boston, MA 02110
                Telecopy:  (617) 434-1153
                Attention:  Mary Reilly

                if to Atlantic Equity Corporation
                c/o NationsBank, N.A. (South)
                One Financial Plaza, 10th Floor
                Fort Lauderdale, FL 33394
                Telecopy: (954) 765-2026
                Attention: Alexander Rody

   8.8.  The Company recognizes that the rights of the Holders under this
Agreement are unique, and, accordingly, the Holders will, in addition to such
other remedies as may be available to them at law or in equity, have the right
to enforce their rights hereunder by actions for injunctive relief and specific
performance to the extent permitted by law.  This Agreement is not intended to
limit or abridge any rights of the Holders which may exist apart from this
Agreement.

   8.9.  The Company agrees that so long as any Securities purchased hereunder
remain outstanding the Company will furnish to each of the Holders all of the
information and reports required to be furnished to the Lenders pursuant to
Section 6.4 of the Credit Agreement as in effect on the date hereof.

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        IN WITNESS WHEREOF, the parties hereto, intending to be legally bound
by the terms hereof, have caused this Agreement to be executed, under seal, as
of the date first above written by their officers or other representatives
thereunto duly authorized.

THE COMPANY                     AMERIPATH, INC.

                                By /s/  Robert P. Wynn
                                   ------------------------------------
                                    Title: EXECUTIVE VICE PRESIDENT AND
                                          CHIEF FINANCIAL OFFICER

THE BANKS:                      THE FIRST NATIONAL BANK OF BOSTON


                                By   /s/ Randy J. Wehling
                                   ------------------------------------
                                    Title: Vice President


                                NATIONSBANK, N.A. (SOUTH)



                                By:  /s/ Steven I. Rody
                                   ------------------------------------ 
                                    Title: Vice President


THE HOLDERS:                    FSC CORP.

                                By:  /s/ Mary Joseph Reilly
                                   ------------------------------------
                                    Title:  Vice President
                                          -----------------------------


                                ATLANTIC EQUITY CORPORATION


                                By:  /s/ John E. Mack
                                   ------------------------------------
                                    Title:  President
                                          
