Chill pineapple and coconut milk. Put all ingredients in an ice cream maker and follow manufacturer's instructions.
This will make too much to freeze all at once, so you'll have to suffer and eat the excess as it grows out of the middle. (Poor you!)
Too much rum/alcohol will cause the ice cream to not freeze properly. Do not use more than a couple tablespoons. You can omit the rum altogether.
Coconut: Although classified by the FDA as a tree nut, coconut is not a common allergen and is not related to tree nuts. If you have a tree nut allergy, consult your physician to find out if you need to avoid coconut.