Rice was a longtime member of the Angels' organization. After retiring as a player, he was retained as their first base coach from 1962 to 1966. He spent the 1967 season as a coach for the Cleveland Indians, but then returned to the Angels as a minor league manager and had success at the Triple-A level. He was named Minor League Manager of the Year for 1971 by The Sporting News after leading the Salt Lake City Bees to a divisional title in the Pacific Coast League.