Mix together the pineapple and sugar in a medium saucepan. Bring it to a boil on medium and stir occasionally. Reduce the heat to medium-low, and simmer while stirring occasionally, until it's soft and slightly thick. Remove from the heat, and let it cool.

Put the mixture in a blender, and add the coconut cream, zest, and juice, and process until it's smooth. Pour the mixture into the bowl of an electric ice cream maker, and freeze according to manufacturer’s instructions. Serve immediately, or freeze for later use.