Thomas Toms and His Kentucky Kin states that Eliza Williams is the daughter of John Haley Williams and Elizabeth Hayes.Like (apparently) many Toms/Tomes researches, I have found this connection to be a dead end.
However, we have found new information that the "book" is incorrect in this case.While we are still working on validating this information in full (there are spelling drifts etc. betwen our sources)
Eliza Williams father:John PAUL or HALEY Williams (sources conflict) grandparents:Samuel Morgan Williams and Millicent "Milly" Cummings great-grandparents:John H. Williams and Martha Woosley gg-grandparents incl. Samuel Woosley and Pheobe Bailey mother:Elizabeth BYERS or BYRES grandparents:John Meade Byers and Eliza Carwile (also spelled Carlyle and Carlisle in Tomes/Toms records).
Samuel Williams, wife Milly, and son John H. are in the 1850 Grayson County KY census but not 1860.John Byers and family (Eliza died in childbirth in 1856) are in the 1860 Grayson County KY census, and one researcher on Rootsweb has supplied additional ancestry information.
John and Elizabeth Williams and Eliza plus two siblings are in the 1880 census in Short Creek, Grayson County, Kentucky.
While I'm not 100% sure of this, the information appears to have higher reliability than what has been posted from other sources and can be substantiated in part from census information and other family trees.