Place undrained pineapple and cream of coconut in largecontainer.

Combine sugar and water.

Bring to boil over medium heat and boil 1 minute.

Cool.

Add sugar syrup and rum to pineapple mixture.

Freeze until firm, about 4 to 6 hours.

Process in blender or food processor until smooth but not completely thawed.

Freeze until firm.

Soften lightly before serving.