Ancestral File has Martha E. Beasley's mother Mary Mitchell, b about 1797 VA. Her mother died 13 May 1864 at Hickman Co., TN. Martha's grandfather Barnet Beasley's wife was Susannah Baugh born about 1769 and died 1840/1850.
There is a user submitted ancestral file that list his parents as James Booker and Serena Chappell that might be worth pursuing. Serena is in the census in TN in 1860 and 1870 - but no James in household.
User Submitted Pedigrees
Citing This Record "Pedigree Resource File", database, FamilySearch (http://familysearch.org/pal:/MM9.2.1/949D-K1W
name: James Booker
father: (Unknown) Booker
mother: Lavaisey (Unknown)
spouse: Sarena Chappell
father: Drury Chappell
mother: Sarah Sexton
child : Willis Booker gender: male
birth: 7 March 1827 Tennessee
death: 24 December 1912 Tennessee
burial: Little Rock Cemetery, (Hickman County), Tennessee
Spouse Martha E. Beasley
birth: 26 August 1826
marriage: about 1851
death: after 14 June 1880