His gravestone has the dates 5 Oct 1827 - 8 Aug 1904, but census records are more consistent with a birthdate in Oct 1826.

Be careful not to confuse him with Benjamin S. Hamilton born Oct 1822, who married Nancy Fairchild.

I do not know for sure the parents of this one. Many online family trees list him as the son of David K. Hamilton and Drucilla Hill. If so, however, he was recorded twice in the 1850 census, once in Morgan County with his wife and children, and once in Carter County with his parents. (Unfortunately, the 1850 census did not record marital status.)

Her gravestone has the dates 20 July 1825 - 10 Dec 1907, but census records are more consistent with a birthdate in July 1824.

Morgan Co., Ky marriage records list the marriage on 5 Feb 1848 of Benjamin S. Hamilton and Julianna Keeton, by W. W. Brown.

1850 census of Morgan Co., Ky, enumerated 29 Aug, lists on p. 76 as family #487:
Benjamin Hamilton Jr., 23, laborer; Julian, 25; Wallace, 1. All born in Kentucky.

The preceding household is that of Julia’s parents, Nelson and Sarah Keeton. The one before that is Benjamin Hamilton age 44 with wife Elizabeth (Nickell) age 43, but they are unlikely to be this Benjamin’s parents, since they have a son Benjamin age 7. Also they were married on 18 Sep 1828.

1860 census of Morgan Co., Ky, district 1, West Liberty P.O., enumerated 7 July, lists on p. 50 as family #305/302:
Benjamin Hamilton, 33, farmer; Juliann, 35; Wallace, 11; Sarrah A, 9; Nancy J., 7; Joseph, 5; Edward, 3; Harvey R., 2. All born in Kentucky.

The daughter recorded here as “Nancy J” must be the one named as Samantha on her birth record and in the 1870 census. Perhaps the census taker misheard “Manthy” as “Nancy”?

1870 census of Morgan Co., Ky, River precinct, enumerated 7 July, lists on p. 7 as family #42:
Hamilton, Benj, 46, farmer; Julia A., 48; Wallace B., 21; Samantha, 17; Joseph, 15; Edward A. (or H.), 13; Harvey B., 12; Nancy, 10; Saml D., 5; William W., 3. All born in Kentucky.

1880 census of Morgan Co., Ky, Elk Fork precinct, enumerated 17 June, lists on p. 22 as family #163/165:
Hamilton, Benj S., 53, farmer; Julia A., 55; Nancy E., 19; Samuel D., 15; William W., 13. All born Ky Ky Ky.

The preceding household is their son Joseph Ray with his wife Nancy. The following household is that of Samuel Hamilton age 61 with wife Cynthia Hill age 55.

1900 census of Morgan Co., Ky, lists with the family of Winston Conley and Sarah A. (Hamilton):
Hamilton, Ben, father-in-law, 73, b. Oct 1826, Ky Ky Ky; Jula, mother-in-law, 75, b. July 1824, Ky Tenn Tenn.

Also on the same page are families headed by their sons Joseph, Wallace, and Samuel, and by Ben Hamilton born July 1863, son of Samuel Hamilton and Cynthia Hill.