<PAGE>   1
                                                                     EXHIBIT 4.6

                                SECOND AMENDMENT
                                       TO
                          REGISTRATION RIGHTS AGREEMENT

THIS AMENDMENT, dated as of February __, 2001 (this "Amendment"), to
REGISTRATION RIGHTS AGREEMENT, dated as of September 21, 1998, as amended by
amendment dated January 5, 1999 (as amended, the "Registration Rights
Agreement"), among (i) Central Parking Corporation, a Tennessee corporation (the
"Company"), (ii) Apollo Real Estate Investment Fund II, L.P., a Delaware limited
partnership (together with its Affiliates, "Apollo"), (iii) AEW Partners, L.P.,
a Delaware limited partnership (together with its Affiliates, "AEW"), and (iv)
Monroe J. Carell, Jr., The Monroe Carell, Jr. Foundation, Monroe Carell, Jr.
1995 Grantor Retained Annuity Trust, Monroe Carell, Jr. 1994 Grantor Retained
Annuity Trust, The Carell Children's Trust, The 1996 Carell Grandchildren's
Trust, The Carell Family Grandchildren 1990 Trust, The Kathryn Carell Brown
Foundation, The Edith Carell Johnson Foundation, The Julia Carell Stadler
Foundation, 1997 Carell Elizabeth Brown Trust, 1997 Ann Scott Johnson Trust,
1997 Julia Claire Stadler Trust, 1997 William Carell Johnson Trust, 1997 David
Nicholas Brown Trust and 1997 George Monroe Stadler Trust (together with their
respective Affiliates other than the Company, the "Carell Holders"). Capitalized
terms used herein without definition have the terms ascribed to them in the
Registration Rights Agreement.

                                   WITNESSETH

WHEREAS, the parties to the Registration Rights Agreement have determined to
further amend it in certain respects, all such parties representing that they
have obtained all necessary approvals to do so;

         NOW, THEREFORE, in consideration of the covenants and agreements of the
Company, Central Sub and Holdings contained in the Merger Agreement and for
other good and valuable consideration, the receipt and sufficiency of which are
hereby acknowledged, the parties hereto agree as follows:

         1.       The Registration Rights Agreement is further amended in the
following respects:

                  (A)      Section 3(b)(i) is hereby amended by adding the
                           following paragraph immediately following the first
                           paragraph:

                  "In the event the Carell Holders elect not to include their
         Registrable Securities under the Shelf at the Initial Filing Date, the
         Carell Holders may request at any time after the Initial Filing Date
         that the Company file a new shelf registration statement on Form S-3
         (the "Second Shelf") for an offering to be made on a delayed or
         continuous basis pursuant to Rule 415 under the Securities Act (or any
         similar rule that may be adopted by the SEC) and permitting sales in
         ordinary course brokerage or dealer transactions not involving an
         Underwritten Offering. Upon receipt of such a request, the Company
         shall use its reasonable best efforts to promptly process, file and
         cause to become effective the Second Shelf. Notice of this request will
         also be simultaneously provided to the Allright Holders. The Second
         Shelf shall give the Carell Holders the right to resell their
         Registrable Securities which could have been included in the Shelf, but
         were not included, on the


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         Initial Filing Date. In the event the Carell Holders make such a
         request, the aggregate Market Value shall be determined as of the
         Initial Filing Date. All of the other provisions of this Agreement also
         shall be applicable to the Second Shelf, including, the provisions of
         Section 3(b) which place limitations on the right of the Carell Holders
         to resell Registrable Securities under certain circumstances. The
         Company further agrees that if it takes any action under Sections 4,
         6(a) or 7(m) with respect to the Shelf, it also will take such action
         with respect to the Second Shelf."

                  (B)      Section 3(b)(v) is hereby amended by changing the
                           defined term "Second Shelf" to "Third Shelf" and all
                           uses of the defined term Second Shelf shall be
                           changed to the defined term Third Shelf.


         2.       This Amendment may be executed in any number of counterparts
and by the parties hereto in separate counterparts, each of which when so
executed shall be deemed to be an original and all of which taken together shall
constitute one and the same agreement.

         3.       This Amendment shall be governed by and construed in
accordance with the laws of the State of Delaware applicable to contracts made
and to be performed wholly within that State.

         4.       Except to the extent specifically modified in this Amendment,
all of the terms and provisions of the Registration Rights Agreement, and the
parties' respective rights thereunder, shall remain in full force and effect and
shall be deemed to apply to this Amendment.

         5.       Two of the original parties named as Carell Holders in the
Registration Rights Agreement no longer exist, but the Registrable Shares held
by such original parties have been transferred to three new Carell Holders who
are now named below as parties to this Amendment.


                 [Remainder of page intentionally left blank.]


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     IN WITNESS WHEREOF, the parties have executed this Agreement as of the date
first written above.

                               CENTRAL PARKING CORPORATION



                               By:      /s/ Monroe J. Carell, Jr.
                                        ---------------------------------------
                               Name:    Monroe J. Carell, Jr.
                               Title:   Chief Executive Officer and
                                                Chairman of the Board


                               MONROE J. CARELL, JR.



                               /s/ Monroe J. Carell, Jr.
                               ------------------------------------------------


                               THE CARELL CHILDREN'S TRUST

                               By:  Equitable Trust Company, Successor Trustee
                                    U/A Monroe Carell, Jr. dated 10/30/87



                                    By:  /s/ M. Kirk Scobey, Jr.
                                         ---------------------------------------
                                         Name:  M. Kirk Scobey, Jr.
                                         Title: Executive Vice President



                               THE 1996 CARELL GRANDCHILDREN'S
                               TRUST F/B/O JULIA CLAIRE STADLER



                               By:      /s/ L. Glenn Worley
                                        ----------------------------------------
                               Name:    L. Glenn Worley
                               Title:   Co-Trustee U/A Monroe Carell, Jr. dated
                                        2/20/96



<PAGE>   4



                            By:      /s/ Kathryn Carell Brown
                                     -------------------------------------------
                            Name:    Kathryn Carell Brown
                            Title:   Co-Trustee U/A Monroe CareIl, Jr. dated
                                     2/20/96


                            By:      /s/ Julia Carell Stadlcr
                                     -------------------------------------------
                            Name:    Julia Carell Stadlcr
                            Title:   Co-Trustee U/A Monroe Carell, Jr. dated
                                     2/20/96


                            By:      /s/ Edith Carell Johnson
                                     -------------------------------------------
                            Name:    Edith Carell Johnson
                            Title:   Co-Trustee U/A Monroe CareIl, Jr. dated
                                     2/20/96


                            THE 1996 CARELL GRANDCHILDREN'S
                            TRUST F/B/O CARELL ELIZABETH BROWN


                            By:      /s/ L. Glenn Worley
                                     -------------------------------------------
                            Name:    L. Glenn Worley
                            Title:   Co-Trustee U/A Monroe Carell, Jr. dated
                                     2/20/96


                            By:      /s/ Kathryn Carell Brown
                                     -------------------------------------------
                            Name:    Kathryn Carell Brown
                            Title:   Co-Trustee U/A Monroe CareIl, Jr. dated
                                     2/20/96


                            By:      /s/ Julia Carell Stadler
                                     -------------------------------------------
                            Name:    Julia Carell Stadler
                            Title:   Co-Trustee U/A Monroe Carell, Jr. dated
                                     2/20/96


                            By:      /s/ Edith Carell Johnson
                                     -------------------------------------------
                            Name:    Edith Carell Johnson
                            Title:   Co-Trustee U/A Monroe CareIl, Jr. dated
                                     2/20/96



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                            THE 1996 CARELL GRANDCHILDREN'S
                            TRUST F/B/O DAVID NICHOLAS BROWN


                            By:      /s/ L. Glenn Worley
                                     -------------------------------------------
                            Name:    L. Glenn Worley
                            Title:   Co-Trustee U/A Monroe Carell, Jr. dated
                                     2/20/96


                            By:      /s/ Kathryn Carell Brown
                                     -------------------------------------------
                            Name:    Kathryn Carell Brown
                            Title:   Co-Trustee U/A Monroe CareIl, Jr. dated
                                     2/20/96


                            By:      /s/ Julia Carell Stadler
                                     -------------------------------------------
                            Name:    Julia Carell Stadler
                            Title:   Co-Trustee U/A Monroe Carell, Jr. dated
                                     2/20/96


                            By:      /s/ Edith Carell Johnson
                                     -------------------------------------------
                            Name:    Edith Carell Johnson
                            Title:   Co-Trustee U/A Monroe CareIl, Jr. dated
                                     2/20/96

                            THE 1996 CARELL GRANDCHILDREN'S
                            TRUST F/B/O WILLIAM CARELL JOHNSON


                            By:      /s/ L. Glenn Worley
                                     -------------------------------------------
                            Name:    L. Glenn Worley
                            Title:   Co-Trustee U/A Monroe Carell, Jr. dated
                                     2/20/96


                            By:      /s/ Kathryn Carell Brown
                                     -------------------------------------------
                            Name:    Kathryn Carell Brown
                            Title:   Co-Trustee U/A Monroe CareIl, Jr. dated
                                     2/20/96




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                            By:      /s/ Julia Carell Stadler
                                     -------------------------------------------
                            Name:    Julia Carell Stadler
                            Title:   Co-Trustee U/A Monroe Carell, Jr. dated
                                     2/20/96


                            By:      /s/ Edith Carell Johnson
                                     -------------------------------------------
                            Name:    Edith Carell Johnson
                            Title:   Co-Trustee U/A Monroe CareIl, Jr. dated
                                     2/20/96


                            THE 1996 CARELL GRANDCHILDREN'S
                            TRUST F/B/O GEORGE MONROE STADLER


                            By:      /s/ L. Glenn Worley
                                     -------------------------------------------
                            Name:    L. Glenn Worley
                            Title:   Co-Trustee U/A Monroe Carell, Jr. dated
                                     2/20/96


                            By:      /s/ Kathryn Carell Brown
                                     -------------------------------------------
                            Name:    Kathryn Carell Brown
                            Title:   Co-Trustee U/A Monroe CareIl, Jr. dated
                                     2/20/96


                            By:      /s/ Julia Carell Stadler
                                     -------------------------------------------
                            Name:    Julia Carell Stadler
                            Title:   Co-Trustee U/A Monroe Carell, Jr. dated
                                     2/20/96


                            By:      /s/ Edith Carell Johnson
                                     -------------------------------------------
                            Name:    Edith Carell Johnson
                            Title:   Co-Trustee U/A Monroe CareIl, Jr. dated
                                     2/20/96




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                              THE CARELL FAMILY GRANDCHILDREN
                              1990 TRUST F/B/O JULIA CLAIRE STADLER

                              By: Equitable Trust Company, Successor
                                  Trustee U/A Monroe Carell, Jr. dated
                                  12/26/90


                                  By:     /s/ M. Kirk Scobey, Jr.
                                          --------------------------------------
                                  Name:   M. Kirk Scobey, Jr.
                                  Title:  Executive Vice President



                              THE CARELL FAMILY GRANDCHILDREN
                              1990 TRUST F/B/O GEORGE MONROE STADLER

                              By: Equitable Trust Company, Successor Trustee
                                  U/A Monroe Carell, Jr. dated 12/26/90


                                  By:     /s/ M. Kirk Scobey, Jr.
                                          --------------------------------------
                                  Name:   M. Kirk Scobey, Jr.
                                  Title:  Executive Vice President



                              THE CARELL FAMILY GRANDCHILDREN
                              1990 TRUST F/B/O CARELL ELIZABETH BROWN

                              By: Equitable Trust Company, Successor
                                  Trustee U/A Monroe CareIl, Jr. dated
                                  12/26/90


                                  By:     /s/ M. Kirk Scobey, Jr.
                                          --------------------------------------
                                  Name:   M. Kirk Scobey, Jr.
                                  Title:  Executive Vice President



<PAGE>   8



                           THE CARELL FAMILY GRANDCHILDREN
                           1990 TRUST F/B/O DAVID NICHOLAS BROWN

                           By: Equitable Trust Company, Successor Trustee
                               U/A Monroe Carell, Jr. dated 12/26/90


                               By:     /s/ M. Kirk Scobey, Jr.
                                       -----------------------------------------
                               Name:   M. Kirk Scobey, Jr.
                               Title:  Executive Vice President

                           THE CARELL FAMILY GRANDCHILDREN
                           1990 TRUST F/B/O WILLIAM CARELL JOHNSON

                           By: Equitable Trust Company, Successor
                               Trustee U/A Monroe CareIl, Jr. dated 12/26/90


                               By:     /s/ M. Kirk Scobey, Jr.
                                       -----------------------------------------
                               Name:   M. Kirk Scobey, Jr.
                               Title:  Executive Vice President

                           THE CARELL FAMILY GRANDCHILDREN
                           1990 TRUST F/B/O ANN SCOTT JOHNSON

                           By: Equitable Trust Company, Successor
                               Trustee U/A Monroe CareIl, Jr. dated
                               12/26/90


                               By:     /s/ M. Kirk Scobey, Jr.
                                       -----------------------------------------
                               Name:   M. Kirk Scobey, Jr.
                               Title:  Executive Vice President

                           THE MONROE CARELL, JR. FOUNDATION


                           By:      /s/ Monroe J. Carell, Jr.
                                    --------------------------------------------
                           Name:    Monroe J. CareIl, Jr.
                           Title:   President



<PAGE>   9



                                   THE KATHRYN CARELL BROWN
                                   FOUNDATION


                                   By:      /s/ Kathryn Carell Brown
                                            ------------------------------------
                                   Name:    Kathryn Carell Brown
                                   Title:   Chairman, Board of Trustees


                                   THE EDITH CARELL JOHNSON FOUNDATION



                                   By:      /s/ Edith Carell Johnson
                                            ------------------------------------
                                   Name:    Edith CareIl Johnson
                                   Title:   Chairman, Board of Trustees


                                   THE JULIA CARELL STADLER FOUNDATION



                                   By:      /s/ Julia Carell Stadler
                                            ------------------------------------
                                   Name:    Julia Carell Stadler
                                   Title:   Chairman, Board of Trustees

                                   1999 KATHRYN CARELL BROWN FAMILY
                                   TRUST

                                   By:      Equitable Trust Company, Trustee U/A
                                            Monroe CareIl, Jr. dated __/99



                                            By:     /s/  M. Kirk Scobey, Jr.
                                                    ----------------------------
                                            Name:   M. Kirk Scobey, Jr.
                                            Title:  Executive Vice President



<PAGE>   10



                                   1999 EDITH CARELL JOHNSON FAMILY
                                   TRUST

                                   By:      Equitable Trust Company, Trustee U/A
                                            Monroe CareIl, Jr. dated __/99



                                            By:     /s/ M. Kirk Scobey, Jr.
                                                    ----------------------------
                                            Name:   M. Kirk Scobey, Jr.
                                            Title:  Executive Vice President


                                   1999 JULIA CARELL STADLER FAMILY TRUST

                                   By:      Equitable Trust Company, Trustee U/A
                                            Monroe CareIl, Jr. dated __/99



                                            By:     /s/ M. Kirk Scobey, Jr.
                                                    ----------------------------
                                            Name:   M. Kirk Scobey, Jr.
                                            Title:  Executive Vice President


                                   1997 CARELL ELIZABETH BROWN TRUST



                                   By:      /s/ L. Glenn Worley
                                            ------------------------------------
                                   Name:    L. Glenn Worley
                                   Title:   Trustee U/A Kathryn Carell Brown and
                                            David H. Brown dated 12/23/97



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                                   1997 DAVID NICHOLAS BROWN TRUST



                                   By:      /s/ L. Glenn Worley
                                            ------------------------------------
                                   Name:    L. Glenn Worley
                                   Title:   Trustee U/A Kathryn Carell Brown and
                                            David H. Brown dated 12/23/97


                                   1997 WILLIAM CARELL JOHNSON TRUST



                                   By:      /s/ L. Glenn Worley
                                            ------------------------------------
                                   Name:    L. Glenn Worley
                                   Title:   Trustee U/A Edith Carell Johnson and
                                            David B. Johnson dated 12/23/97


                                   1997 ANN SCOTT JOHNSON TRUST



                                   By:      /s/ L. Glenn Worley
                                            ------------------------------------
                                   Name:    L. Glenn Worley
                                   Title:   Trustee U/A Edith Carell Johnson and
                                            David B. Johnson dated 12/23/97


                                   1997 GEORGE MONROE STADLER TRUST



                                   By:      /s/ L. Glenn Worley
                                            ------------------------------------
                                   Name:    L. Glenn Worley
                                   Title:   Trustee U/A Julia Carell Stadler and
                                            George B. Stadler dated 12/23/97





<PAGE>   12



                          1997 JULIA CLAIRE STADLER TRUST


                          By:      /s/ L. Glenn Worley
                                   ---------------------------------------------
                          Name:    L. Glenn Worley
                          Title:   Trustee U/A Julia Carell Stadler and
                                   George B. Stadler dated 12/23/97


                          APOLLO REAL ESTATE INVESTMENT FUND II, L.P.

                          By:      Apollo Real Estate Advisors II, L.P.,
                                   its general partner

                          By:      Apollo Real Estate Capital Advisors II, Inc.,
                                   its general partner



                                   By:     /s/ Williams S. Benjamin
                                           -------------------------------------
                                   Name:   William S. Benjamin
                                   Title:  Vice President


                          AEW PARTNERS, L.P.

                          By:      AEW/L.P., its general partner By: AEW, Inc.,
                                   its general partner



                                   By:     /s/ Marc Davidson
                                           -------------------------------------
                                   Name:   Marc Davidson
                                   Title:  Vice President