Add cream of coconut, ½ cup pineapple chunks, rum, and ice cubes to FourSide jar in order listed. Secure lid and select "Ice Crush."
Pour mixture into ice-pop molds, filling ¾ full. Mix together remaining pineapple chunks, coconut flakes, and lime zest; and add to molds. Freeze ice pops until solid.
For an alcohol-free version, substitute 4 ounces skim milk or coconut milk for rum.