<PAGE>   1




                                                    ----------------------------
                                                           OMB APPROVAL
                                                    ----------------------------
                                                    OMB Number:        3235-0145
                                                    Expires:     August 31, 1991
                                                    Estimated average burden 
                                                    hours per response ....14.90
                                                    ----------------------------


                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                              WASHINGTON, D.C. 20549

                                  SCHEDULE 13G

                   UNDER THE SECURITIES EXCHANGE ACT OF 1934

                                (AMENDMENT NO. 7)*


                               Kirby Corporation
- --------------------------------------------------------------------------------
                                (Name of Issuer)


                                 Common Shares
- --------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                    497266106
                            -------------------------
                                 (CUSIP Number)

Check the following box if a fee is being paid with this statement [ ]. (A fee
is not required only if the filing person: (1) has a previous statement on file
reporting beneficial ownership of more than five percent of the class of
securities described in Item 1; and (2) has filed no amendment subsequent
thereto reporting beneficial ownership of five percent or less of such class.)
(See Rule 13d-7).

*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter the
disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).



                               Page 1 of 8 pages



<PAGE>   2

CUSIP No. 497266106                       13G                  Page 2 of 3 Pages



- --------------------------------------------------------------------------------
 1    NAME OF REPORTING PERSON 
      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSONS

      Luther King Capital Management Corporation    I.R.S. Identification No.
      301 Commerce, Suite 1600                      #75-0163033      
      Fort Worth, TX 76102

- --------------------------------------------------------------------------------
 2    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*

      Shares are owned in accounts for the benefit of children of        (a) [ ]
      certain Luther King Capital Management employees and certain 
      Luther King Capital Management employees.                          (b) [X}

- --------------------------------------------------------------------------------
 3    SEC USE ONLY



- --------------------------------------------------------------------------------
 4    CITIZENSHIP OR PLACE OF ORGANIZATION

      Fort Worth, Texas

- --------------------------------------------------------------------------------
                               5     SOLE VOTING POWER

          NUMBER OF                  1,876,607 Luther King Capital Management
                                     1,150 Bryan King
           SHARES                    1,150 Mason King

        BENEFICIALLY           -------------------------------------------------
                               6     SHARED VOTING POWER
          OWNED BY

            EACH
                               ------------------------------------------------
          REPORTING            7     SOLE DISPOSITIVE POWER

           PERSON                    1,876,607 Luther King Capital Management
                                     1,150 Bryan King
            WITH                     1,150 Mason King

                               ------------------------------------------------
                               8     SHARED DISPOSITIVE POWER                  
        

- ------------------------------------------------------------------------------- 
 9    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

      1,878,907 
        
- --------------------------------------------------------------------------------
10    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*


- --------------------------------------------------------------------------------
11    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

      9.0%

- --------------------------------------------------------------------------------
12    TYPE OF REPORTING PERSON*

      IA

- --------------------------------------------------------------------------------

                     * SEE INSTRUCTION BEFORE FILLING OUT!


                              Page 2 of 8 pages



<PAGE>   3


                                                                     Page 3 of 3

                                 CERTIFICATION

By signing below I certify that, to the best of my knowledge and belief, the
securities referred to above were acquired in the ordinary course of business
and were not acquired for the purpose of and do not have the effect of changing
or influencing the control of the issuer of such securities and were not
acquired in connection with or as a participant in any transaction having such
purposes or effect.

                                   SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief, I certify
that the information set forth in this statement is true, complete and correct.



                                                    February 10, 1999
                                              ----------------------------------
                                                          Date


                                                    /s/ LUTHER KING
                                              ----------------------------------
                                                        Signature



                                                    Luther King/President
                                              ----------------------------------
                                                          Name/Title