Cooper was born November 1, 1815, most likely in Amite County, Mississippi. His father, David Cooper, was a physician and Baptist minister. His mother was Sarah Davenport. Cooper attended the University of Virginia from 1832 until 1834; his classmates included future Civil War generals Carnot Posey, Lafayette McLaws, and John B. Magruder. Cooper returned home to take up farming on "Mon Clova", his plantation in Wilkinson County, Mississippi in the Cold Springs community, which was a tiny village between Woodville and Natchez. He married Mary Collins of Natchez and had 7 children. Entering politics, he was elected in 1844 to serve as a Whig in the Mississippi State Legislature.