His death certificate records Joseph Peyton, age 77 years 4 months 11 days, born 26 June 1844 in Morgan Co., Ky, died 7 Nov 1921 in Panama, Salem township, Morgan Co., Kentucky, married, minister, father Western Peyton, born in Alabama, mother’s maiden name Elisabeth Gevedon, born in Ky, cause of death cancer of the liver, informant Dan Peyton, Nickell, Ky, burial in Gevedon Cemetery.

Joseph and Carrie were first cousins on the Gevedon side (their mothers were sisters).

1870 census of Morgan Co., Ky, Grassy precinct, Hazle Green P.O., enumerated 19 Aug, lists on p. 13 as family #77/78:
Peyton, Joseph, 25, farmer; Cary A., 21; John A., 2. All born in Kentucky.

(Hazel Green is right on the border of Morgan and Wolfe counties, part of it in each county.)

I cannot find this family in the 1880 census. (Besides searching on anyone with a surname of P*t?n, and every given name in the family surname unspecified, I also looked at the pages in 1880 that contained the people who were their neighbors in 1870 or 1900.)

1900 census of Morgan Co., Ky, district 3, enumerated 20 June, lists on p. 17A as family #224/225:
Peyton, Joseph, 55, b. June 1844, farmer; Cary A., wife, 52, b. Oct 1847, married 34 years, mother of 10 children, 7 living; Western, son, 25, b. July 1874; George W., son, 22, b. May 1878; Caroline A., dau, 17, b. Oct 1882; Greenberry F., son, 14, b. Aug 1885; Ellis E., son, 10, b. Jan 1890. All born Ky Ky Ky.

The next household is headed by their son John.

1910 census of Morgan Co., Ky, Salen precinct, enumerated 20 April, lists on p. 2A as family #15:
Payton, Joe, 65, farmer; Carsia, wife, 62, first marriage for both, married 44 years, mother of 10 children, 7 living; George W., son, 31, single, farmer; Green B., son, 24, married, farmer; Ethel, dau-in-law, first marriage for both, married 1 year, mother of 1 child, 1 living; Leonard, grandson, 6/12; Ellis, son, 20, single, farm laborer. Gevedon, Anderson, son-in-law, 22, farmer; Caroline, dau, 27, first marriage for both, married 2 years, mother of 1 child, 1 living; Lonna, grandson, 11/12. All born Ky Ky Ky.