I have a William A. CONSTANT, b. ca. 1844 in KY, but I have nothing more on him.He "might be" your man.If so, he was the son of William Bryson CONSTANT and his wf. Delila CARROLL.Do you know any more about your William A. than what you posted....names of some of his siblings, etc.?
William Bryson and Delila (CARROLL) CONSTANT lived in Hardin Co., KY in 1840, 1860 and 1870.In 1850, they were in Larue Co., KY and, in 1880, they were in Edmonson Co., KY. These counties are in near proximity to Meade Co..
If you think this is the right family, I'd love to exchange info with you.