My only connection to this family is that their daughter Susan married my second cousin 5 times removed, James William Lowry/Lowery, who is related to me through our Sexton line.

I’m entering more data on their descendants than I usually do for in-laws of distant cousins, because there is a discrepancy between the birth and death records for Susan - the former records her parents as William K. Conner and Martha A. Willson, while the latter records her father as Kirk Cannon and her mother’s name as unknown.

The birth and death records for William and Martha’s other children, especially those of Mary Jane and the unnamed child stillborn in 1859, provide evidence to support my conclusion that the surname Conner is incorrect on Susan’s (and Mary Jane’s) birth record.

1850 census of Bath Co., Ky, district 1, enumerated 3 Sep, lists on p. 81 as family #572:
William K. Cannon, 38, farmer; Martha A., 23; Zachariah T., 2; Charles N., 1. All born in Kentucky.

The 1860 situation is very strange for this family. There is a Kirkman Cannon family in Bath Co., but the age for Kirkman is 10 years younger, the wife’s name is wrong, and none of the other family members match the data suggested by the 1850 or 1870 censuses or the birth records. So the most obvious conclusion would be that it is a different Kirkman Cannon, perhaps a cousin. I still think that is the most likely explanation. On the other hand, I can find no match for anyone in the “other” Kirkman Cannon family in any other census year nor in the birth records, and some of them should fall in the 1852 to 1859 period for which birth records are available.

Here is that mystery family:
1860 census of Bath Co., Ky, Owingsville P.O., enumerated 3 Aug, lists on p. 181 as family #1309:
Kirkman Cannon, 38, farmer; Polly, 36; Susan, 12; David, 9; Alexander, 8; John, 6; Mary, 4; James 1/12; Martha, 2/12. All born in Kentucky.

Many online family trees have merged these two families, but the discrepances are so great that I am going to refrain from doing so.

1870 census of Bath Co., Ky, Bethel precinct, enumerated 21 July, lists on pp. 2-3 as family #14:
Kirkman, Camon, 58, farmer; Martha, 40; John, 9; Fanny, 7; Dennis, 5; Isaac, 4; Samuel, 1. All born in Kentucky.

The census taker apparently misunderstood Kirkman as being a surname instead of a given name.

The preceding household is headed by Dennis Hawkins, age 57, after whom Kirk and Martha named their son.

1880 census of Bath Co., Ky, district 6, enumerated 7 June, lists on p. 14 as family #109:
Cannon, Kirkman, 70, laborer, b. Ky Dela Va; Martha, 55, b. Ky Ky Ohio; John L., 18, son; Dennis, 15, son; Isaac C., 13, son; Samuel, 11, son; Oliver, 9, son; Fanny, 17, dau. All children born Ky Ky Ky.

1900 census of Bath Co., Ky, Bethel precinct, enumerated 12 June, lists on p. 12B as family #228/230:
Cannon, Samuel, 30, b. Apr 1870, farmer; Maggie, wife, 26, b. Aug 1873, married 1 year, mother of 0 children; Martha, mother, 74, b. Apr 1826, widowed, mother of 15 children, 11 living. All born Ky Ky Ky.