The 1900 census records his birthdate as Sep 1843, but he was listed as age 8 in the 1850 census and age 19 in 1860, with enough younger brothers that it would be quite difficult to squeeze them all in if he were born in late 1843.

1870 census of Elliott Co., Ky, precinct 1, Sandy Hook P.O., enumerated 22 June, lists on p. 30 as family #175:
Elliott, Robert, 25, farmer; Martha, 21; James, Emily, 8. All born in Ky.

1880 census of Carter Co., Ky, precinct 8, enumerated 17 June, lists on p. 17, line 17 (this listing does not number the households or families):
Elliott, Robert, 36, farmer; Martha A., wife, 28; Andrew J., son, 8; Aramatha, dau, 5; Elizabeth, dau, 3. All born Ky Ky Ky.

1900 census of Elliott Co., Ky, Devils Fork precinct, enumerated June (undated), lists on p. 2B as family #33:
Elliott, Robert, 56, b. Sep 1843, farmer; Martha A., wife, 54, b. Jan 1846; Della, dau, 14, b. May 1886; Lewis, William H., grandson, 1, b. Apr 1899. All born Ky Ky Ky.

There are three other Elliott families on this page, including Alexander age 46 with wife Martha J., John age 44 with wife Angeline, and John age 29 with wife Mary A.