After graduation, Cooper matriculated at Centre College in Danville, Kentucky. While at Centre, Cooper was accepted into the Beta Theta Pi fraternity. He also played defensive end on the Praying Colonels' football team. Cooper was a letterman on the team, playing alongside football notables Bo McMillan, Red Roberts, Matty Bell, and Red Weaver. Another member of the team, John Y. Brown, Sr., would later become one of Cooper's political rivals. Coached by Charley Moran, the team was undefeated in four games in the 1918 season, which was shortened by an outbreak of the Spanish flu.