<PAGE>   1
                                                                  Exhibit 10.19


                                 FIRST AMENDMENT
                                     TO THE
                              COVENTRY CORPORATION
                     SUPPLEMENTAL EXECUTIVE RETIREMENT PLAN



         The Coventry Corporation Supplemental Executive Retirement Plan (the
"Plan") is hereby amended, effective as of the dates set forth below, as
follows:


         1.       Section 2.8 is amended to clarify its original meaning
and to provide as follows:

                  2.8 Deferred Compensation Account. "Deferred Compensation
         Account" means the account maintained on the books of the Employer to
         which Deferred Compensation and Employer Matching Contributions for
         each Participant are credited, and to which deemed interest, dividends,
         and investment gains are added to the account and the amount of any
         distributions, deemed investment losses, and expenses are deducted from
         the account.


         2.       Section 2.11 is deleted in its entirety.


         3.       Section 2.13 is amended, effective January 1, 1996, to
provide as follows:

                  2.13 Eligible Employee. "Eligible Employee" means an Employee
         who the Compensation Committee of the Board determines is a highly
         compensated employee or a select member of management who, by virtue of
         his position with the Employer, is uniquely informed as to the
         Employer's operations and has the ability to materially affect the
         Employer's profitability and operations. The Compensation Committee may
         determine at any time that an Employee no longer satisfies this
         standard, in which case he shall cease to be an Eligible Employee.

         4.       Sections 2.24 is amended to clarify its original intent
and to provide as follows:

                  2.24     Trust.  "Trust" means the grantor trust which
         is intended to conform to the terms of the model trust
         as described in Revenue Procedure 92-64.  The Trust has
         been established by the Employer for the purpose of


<PAGE>   2



         accepting contributions which may be made under the Plan and to which
         interest, dividends, and investment gains are added and from which the
         amount of any distributions, investment losses, and expenses are
         deducted.


         5.       Article III is amended to clarify its original intent and to 
provide as follows:

                                   ARTICLE III

                          ELIGIBILITY AND PARTICIPATION


                  3.1      Eligibility

                           (a)      Eligibility.  Eligibility to participate
                  in the Plan is limited to Eligible Employees.

                  3.2      Participation

                           (a) Form of Deferral. An Eligible Employee may become
                  a Participant by properly executing a Deferred Compensation
                  Agreement and filing such Agreement with the Committee. An
                  Eligible Employee may elect to defer, in whole percentages, 1%
                  to 15% of his base salary per pay period and 1% to 100% of his
                  bonus for a Plan Year. The Deferred Compensation Agreement
                  shall be executed before the first day of the Plan Year for
                  which the deferred compensation is otherwise payable and shall
                  be effective as of the first day of the first payroll period
                  beginning in such Plan Year; provided, however, that in the
                  first year that an Employee becomes an Eligible Employee, such
                  Eligible Employee may make an election within 30 days after
                  becoming an Eligible Employee to defer Compensation for
                  services to be performed after he becomes an Eligible Employee
                  and such Eligible Employee's Deferred Compensation Agreement
                  shall be effective as of the first day of the payroll period
                  beginning immediately following the execution of such
                  Agreement, or the effective date of such Agreement, if later.

                           (b) Modification of Deferral Compensation Agreements.
                  A Deferred Compensation Agreement will remain in effect until
                  a new Deferred Compensation Agreement is filed with the
                  Committee in accordance with the terms and conditions
                  specified herein or until the date a Participant ceases to be
                  an Eligible Employee. A Deferred Compensation Agreement may
                  only be amended or



                                       2

<PAGE>   3

                  revoked for a subsequent Plan Year by filing a new Deferred 
                  Compensation Agreement with the Committee at least 15 days 
                  (or such shorter period as may be established by the 
                  Committee) before the beginning of the subsequent Plan Year.


         6.       Section 4.2 is amended to clarify its original meaning
and to substitute the word "credit" for the word "contribute" in
the first sentence thereof.


         7.       Section 4.4 is amended to clarify its original meaning
and to provide as follows:

                  4.4 Participant Directed Investment Options. Each Participant
         shall have the opportunity to direct the deemed investment of his
         Deferred Compensation Account among the deemed investment options
         selected by the Committee in multiples of 10% in accordance with which
         deemed interest, dividends and investment gains and losses will be
         added to or deducted from his Deferred Compensation Account. Transfers
         among investment options may be made on a monthly basis throughout the 
         Plan Year, to be effective as of the last day of each calendar month.


         8.       Section 5.3 is amended to clarify its original meaning
by capitalizing the word "Beneficiary" in the first sentence
thereof.


         9. Section 5.5 is amended to clarify its original meaning and to
substitute the reference to "paragraph 5.3(a)" for the reference to "paragraph
5.3(b)" in the last sentence thereof.


         10.      Section 9.3 is amended to clarify its original meaning
and to provide as follows:

                  9.3 Termination of Plan. The Board may at any time terminate
         the Plan with respect to new deferral elections, as to any Eligible
         Employee or in its entirety if, in its judgment, the tax, accounting,
         or other effect of the continuance of the Plan, or any potential
         payment thereunder would not be in the best 




                                       3
<PAGE>   4

         interest of the Employer. If the Plan is terminated in its entirety or
         as to any Eligible Employee, each affected Participant shall be 100%
         vested in the value of his Deferred Compensation Account. Upon such
         termination, each Participant will receive the value of his Deferred
         Compensation Account in the form of a lump-sum payment to be made no
         later than 120 days following the termination date.


         11.      Section 10.3 is amended to clarify its original meaning
and to provide as follows:

                  10.3     Nonassignability.  Neither a Participant nor
         any other person shall have any right to alienate, commute, sell, 
         assign, transfer, pledge, anticipate, mortgage or otherwise encumber,
         transfer, hypothecate or convey in advance of actual receipt the
         amounts, if any, payable hereunder, or any part thereof, which are,
         and all right to which are, expressly declared to be unassignable and
         non-transferrable. No part of the amounts payable shall, prior to
         actual payment, be subject to seizure, attachment, garnishment by
         creditors or separation for the payment of any other person, nor be
         transferable by operation of law in the event of a Participant's or an
         other person's bankruptcy or insolvency.


         IN WITNESS WHEREOF, Coventry Corporation has caused this First
Amendment to the Coventry Corporation Supplemental Executive Retirement Plan to
be executed by its duly authorized officers this 31st day of December, 1996.



                                         COVENTRY CORPORATION



                                         By: /s/ Shirley R. Smith 
                                             -------------------------------


ATTEST:

/s/ J. H. Ockerman
-------------------------


                                       4