1860 census of Montgomery Co., Ky, Mt. Sterling P.O., enumerated in June, lists on p. 42 as family #280:
Wm Williams, 38; Elizabeth, 35; Rebecca, 13; Mary E., 11; Nancy J., 10; Mathen, 6; Jas L., 6; Josephine, 1. All born in Kentucky.

1870 census of Montgomery Co., Ky, Camargo precinct, enumerated 9 Aug, lists on p. 15 as family #99:
Williams, Wm, 49, farmhand, b. Ky; Elizabeth, 35, b. Indiana; N. J., 17; Preston, 14; James, 13; Julia, 8; Isabelle, 4. All children born in Kentucky.

It is probable that this is a second wife also named Elizabeth, since the age and birthplace do not match.