Here's what I could find for you.
Alfred Duke Durham born 22 Jul 1879 in Kentucky, probably Bowling Green, Warren Co.
Parents were Alfred P. Durham born Nov 1840 (may be 1839) in Kentucky and Sarah Charlotte Billingsley born 28 Mar 1844 in Allen Co., Kentucky. They were married 12 May 1869 in Warren Co., Kentucky.
He had 1 brother Claude Billingsley Durham born 09 Jun 1886 in Bowling Green, Warren, Kentucky. he married Frances G. Frost on 16 Jun 1914 in Indianapolis, Where they continued to live.
Alfred P.'s parents were John G. Durham and Caroline Thacker. John was born 15 Nov 1813 in Halifax Co., VA, the son of John Durham and Martha Mullins. Caroline was born 06 Dec 1813 in Allen Springs, Allen, KY. John G. Durham was a Baptist minister.
That's the best I can do for you. Hope it helps.