Preheat oven to 375°F.
Place pineapple chunks into a large bowl and add sugar, rum and allspice.
Toss well and pour into a 9" by 13" baking pan.
Roast for 1 hour, or until pineapple is caramelized and tender.
Place coconut into a shallow bowl and add a scoop of ice cream.
Roll it around until it is coated in coconut.
Repeat for other ice cream balls.
Spoon some pineapple into a serving dish and add ice cream.