	Several members of Cooper's family have competed in rodeo events. His father Tuffy was a PRCA cowboy who was inducted into the National Cowboy Hall of Fame in 1998; he taught roping to Roy when he was a child. Cooper's sister, Betty Gayle, was a champion in cowgirl events and is in the National Cowgirl Hall of Fame. He also had a brother, Clay, who was a professional rodeo cowboy, as was his cousin Jimmie. Cooper has three sons—Clif, Clint, and Tuf—who are cowboys. They all participated in the 2010 NFR's tie-down roping event, making it the first time three brothers had done so. Tuf was the winner of the 2017 PRCA All-Around Cowboy title. Cooper's stepdaughter, Shada, is married to Brazile, a 23-time PRCA world champion.