1Combine all ingredients in a large 2-quart container and stir until thoroughly mixed. Cover and chill in the refrigerator until thoroughly chilled, about 3 hours.
2Once chilled, turn on an ice cream maker and pour in the coconut mixture. Spin in the ice cream maker until thick and slushy, about 20 to 30 minutes. Keep cocktail chilled in the ice cream maker base while serving.