In the food processor, chop the pineapple with 1/4 cup of the sugar and reduce the size of bits to no more than 1/4″. If pineapple is too wet, add more sugar to dry it out. Remove from blender and finish separating the bits with your hands.
Pour the coconut milk in the ice cream maker, and start the machine. After a couple minutes, just before the freezing starts, pour the pineapple bits in the milk. Stop the machine when ice cream is set.