Thank you very much Gordon. I believe that this Thomas A. McCraney is the same as this one:
McCRANEY, THOMAS A. - Age, 28 years. Enlisted, September 14, 1864, at Avon, Livingston, NY; mustered in as private, Co. I, September 14, 1864, to serve three years; discharged, June 23, 1865, at Tarboro, N.C.

Were there any dates on the stone your father recorded?
Sincerely,
John Reed