In a blender container or food processor bowl combine cream of coconut, undrained pineapple, orange juice, and rum. (If using a food processor, process only half of all the ingredients at a time.) Cover; blend or process until nearly smooth. Pour into a 9x5x3-inch loaf dish or a 2-quart baking dish. Cover; freeze about 4 hours or until firm.

Break sherbet into pieces. Place sherbet, about half at a time, in a blender container or food processor bowl. Cover; blend or process until fluffy. (Or, place in a chilled bowl and beat with an electric mixer until fluffy.) Return pineapple mixture to pan. Cover and freeze at least 4 hours or until firm. Makes 4 cups (15 servings).