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.