Reserach has shown me that Paul "Bear" Bryant's mother is
Dora Ida Kilgore Bryant. His father is William Monroe Bryant. I have not been able to determine if any Bryant serving in the CSA is his grandfather, but I believe this man is Bear's grandfather on his mothers side.

William L. Kilgore (First_Last)
Regiment Name 33 Arkansas Infantry
Side Confederate
Company H
Soldier's Rank_In Private
Soldier's Rank_Out Private

Does anyone have an opinion or dispute this research?

Source:
http://encyclopediaofarkansas.net/encyclopedia/entry-detail.aspx?entryID=1604

George