In the 1850 Census for Pulaski County, Kentucky (Division 2), William Durham, age 44 is married to Mary. (Mary "Polly" Baugh). In the same Division 2, there is also a Robertson Vaughn, age 61 married to Elizabeth (Durham). Elizabeth Durham is the daughter of Gregory Durham and Elizabeth Shelton of Henry County, Virginia. (Deed of 1816 - Stokes County, NC) William Durham somehow may connect to this Durham family. More research is needed.
William Durham married for the second time on 25 DEC 1857 in Pettis County, Missouri to Sarilda Ramsey (Missouri Marriage Records, 1805 - 2002-Ancestry.com).
In the 1880 Census for Vernon County, Missouri (Lake - District 215), Sarilda Durham, age 48 is listed as "head of household" and "widowed". She is listed with sons: John W., age 20; Wm R., age 15; and M. A. (Morris), age 13; all born in Missouri.
In the 1900 Census for Limestone County, Texas (Prairie Hill and Mount Antioch - District 54), S. Durham (Sarilda Durham), age 65 and "widowed" is listed as "Mother" in the household of M. A. Durham (Morris A. Durham), age 33, and wife Belle J. (NOTE: There is one small error with the 1900 Census - M. A. Durham shows that his mother was born in "Indiana", but the "Mother" listed, "S. Durham" shows she was born in "Kentucky".)