The Findagrave memorial shows him as the (ONLY?) son of "William A. "Archey" Cole and Lucinda Harden. "
MANY public trees at Ancestry show him as son of John Tate Cole and Sirena Pigg.
I have added him here: William A Cole
https://www.ancestry.com/family-tree/person/tree/416364/person/-175...
https://www.ancestry.com/family-tree/person/tree/47118205/person/69...
https://www.ancestry.com/family-tree/person/tree/117883912/person/4...
etc.