Some online family trees list his parents as Gabriel Jones and Mary Noe of Harlan Co., Ky, while others list him as the son of John Craig Jones and Anna Day. The latter seems more likely.

In 1850 Wiley, Elizabeth and their children were living with a McDaniel family (unless the census enumerator just forgot to enter a new family number):

1850 census of Montgomery Co., Ky, district 2, enumerated 31 July, lists on p. 20 as family #129:
Samuel McDaniel, 24, laborer; Lucinda, 39; Daniel, 5; James, 3; John M., 8/12. Armina Lewis, 12.
Wiley Jones, 27, laborer; Elizabeth, 26; Mary A., 13; Cythia Jane, 11; Rebecca, 9; Ally (f), 7; Susan, 5; Greenberry, 3. All born in Kentucky.

Mary seems too old to be a daughter of Wiley and Elizabeth, but the ages for the girls may be wrong.

1860 census of Breathitt Co., Ky, district 1, Jackson P.O., enumerated 30 July, lists on p. 110 as family #743:
Wiley Jones, 38, farmer, b. Morgan; Elizth, 37, b. Floyd; Pulina, 14; Alles, 13; Greenberry, 12; John D., 9; Nancy E., 6. All children born in Breathitt Co.

The daughter listed here as Pulina is probably the same one listed as Susan in 1850, although if so she has swapped places in the birth order with Alley.

The next household is headed by James Smith, whose daughter Arnetta Jones would later marry Wiley and Elizabeth’s son Greenberry.