When names are fairly common every little bit helps, hope some of this helps to narrow down your search.
TX Dth Idx thru 1976:
Name: Sarah Lee Wright Death Date: 30 Mar 1960 Death Place: Baytown, Harris, Texas Gender: Female Race: Death Age: 70 years Estimated Birth Date: 1890 Birth Date: Birthplace: Marital Status: Spouse's Name: Father's Name: Thomas Richard Williams Father's Birthplace: Mother's Name: Margaret Paralee Carter Mother's Birthplace: Occupation: Place of Residence: Cemetery: Burial Place: Burial Date: Additional Relatives: Film Number: 2116168 Digital Film Number: 4166231 Image Number: 3351 Reference Number: fn 24263
Name: James Richard Williams Death Date: 16 Jun 1943 Death Place: Lockhart, Caldwell, Texas Gender: Male Race: White Death Age: 61 years 9 months 28 days Estimated Birth Date: Birth Date: 18 Aug 1881 Birthplace: Smith County, Texas Marital Status: Married Spouse's Name: Father's Name: Thomas Williams Father's Birthplace: Mother's Name: Parilee Carter Mother's Birthplace: Occupation: Farming Place of Residence: Lockhart, Caldwell, Texas Cemetery: Burial Place: Mcmahan, Texas Burial Date: 17 Jun 1943 Additional Relatives: X Film Number: 2137307 Digital Film Number: 4030098 Image Number: 121 Reference Number: cn 25916
You can add another county -- 1880 census Smith Co, TX:
Williams, J.T., 28, b TX, MS, MS " Marg't, 19, wife, b TX -- -- " Mary, 1, dau, b TX
Maybe one of the other researchers who browse this forum can take this and run with it. I don't have access to some of the records others can use.