Her death certificate records Martha Ellen Bailey, age 87 years 2 months 14 days, born 18 Feb 1850 in Kentucky, died 2 May 1938 in Owingsville, Bath Co., Ky, widow of John S. Bailey, father James Coyle, mother’s maiden name Rebecca Kincaid, both born in Kentucky, cause of death lobar pneumonia, informant Thomas Horseman, Sharpsburg, Ky, burial in Bailey graveyard.

Be careful not to confuse her with Martha E. Hart born 10 Sep 1852, who married Johnson Horseman.

The 1850 census of the James Coyle family included a son Mathew age 3 months. That was probably a mistaken entry for Martha. (The 1860 census lists Marth E age 10 and no Mathew.)

1900 census of Bath Co., Ky, Wyoming precinct, enumerated , lists as family #120:
Bailey, John S., 64, b. June 1835, farmer; Martha E., wife, 49, b. Feb 1851, married 4 years, mother of 6 children, 3 living; Jeff, son, 25, b. Nov 1874. Horseman, Dee N., stepson, 14, b. Oct 1885; Algen T., stepson, 11, b. June 1888. All born Ky Ky Ky.

1870 census of Bath Co., Ky, Wyoming precinct, enumerated 4 Aug, lists on p. 2 as family #15:
Horsman, Omah, 24, farmer; Martha, 19; Maggie B., 1. All born in Kentucky.

I cannot find this family in the 1880 census.