The 1850 census lists the oldest child of Wilson and Celer Fraley as Harrison, age 2, and no William. The 1860 census lists their oldest child as William O. B., age 13, and no Harrison. Possibly Harrison and William are the same person. Another possibility is that he is the William age 4 listed with the widowed Honor Fraley in the 1850 census, and that he is really a nephew rather than a son of Wilson Fraley:

1850 census of Morgan Co. Kentucky lists as family #199:
Honor Fraley, 31; Margaritt, 15; Emily, 10; Marcus, 6; William, 4; Taylor, 1.

Morgan Co., Ky, birth register for 1855 lists Elizabeth M. McDanl, born 26 Mar 1855, father Geo McDaniel, mother’s maiden name Elizabeth Roice.

Her death certificate (Vol. 51, #25351) records Bettie Fraley, age 86 years 7 months 12 days, born 24 Mar 1855 in Rowan Co., Ky, died 7 Oct 1941 in Morehead, Rowan Co., Ky, widowed, father George McDaniel, mother’s maiden name Lizie Rice, both born in Rowan Co., Ky, cause of death double pneumonia, informant Henry Fraley, McRoberts, Ky, burial in family cemetery.

In 1930 she was listed as age 75 with her son Neal.

1880 census of Rowan Co., Ky, Christy Creek precinct, lists as family #409:
Butlor Fraily, 34, farmer; Elizabeth, 25, wife; Elizabeth, 5, dau; William, 3, son; Mollie M., 8 mo., dau. All born in Kentucky.

1900 census of Rowan Co., Ky, Hoggtown precinct, enumerated 8 June, lists on p. 6B as family #106/107:
Fraley, Butler, 53, b. 1847, day laborer; Elizabeth M., wife, 45, b. Mar 1855, married 26 years, mother of 8 children, 7 living; William, 23, b. Feb 1877; Mollie, dau, 20, b. June 1880; Georg. W., son, 17, b. Oct 1882; Henry C., son, 14, b. Mar 1886; Neal R., son, 8, b. Mar 1892; Anna, dau, 5, b. Apr 1895. All born Ky Ky Ky.

1910 census of Rowan Co., Ky, Morehead precinct, enumerated 12 April, lists on p. 1A as family #8:
Fraley, Elizabeth, 54, first marriage, married 36 years, mother of 8 children, 7 living; Cornelius, son, 17; Anna, dau, 15; Mollie, dau, 29, single, mother of 2 children, 2 living; Cora Lee, grandchild, 7; William, grandchild, 2. All born Ky Ky Ky.

1920 census of Rowan Co., Ky, Morehead precinct, enumerated 31 Jan, lists on p. 16B as family #190/194:
Fraley, Bettie Mrs., 65, widowed; George, son, 38, widowed, laborer; Cora, dau, 28, single, laundress; Neal, son, 25, single, laborer. All born Ky Ky Ky.

There is no match in the 1910 or 1900 censuses for a daughter Cora born in the 1890’s. She is probably really the granddaughter Cora listed as age 7 in 1910, daughter of Mollie.