He and his sisters Jane and Jeannette are triplets. Don Shula, who was 6 years old when they were born, jokingly called Jim, Jane, and Jeannette "my first coaching job" in his Pro Football Hall of Fame acceptance speech.
His father immigrated to America from Hungary with his family in 1905. When Dániel Sule's parents decided to return to Hungary, he decided to stay behind. He changed his last name to "Shula" because he thought it sounded more American.