Puree the pineapple in a blender with the sugar, coconut milk, rum, and lime juice. Chill thoroughly for several hours.
Freeze in an ice cream machine according to manufacturer’s directions.
Pour sorbet into a bowl and freeze for several hours to harden before serving.
Note: Look for unsweetened coconut milk in the Asian isle of your grocery store. Do not use products like Coco Lopez, as they are high in sugar.
Calories: 231kcal, Carbohydrates: 42g, Protein: 1g, Fat: 7g, Saturated Fat: 6g, Sodium: 6mg, Potassium: 202mg, Fiber: 2g, Sugar: 37g, Vitamin A: 66IU, Vitamin C: 55mg, Calcium: 20mg, Iron: 1mg