Using a sharp chef's knife, chip the top and the bottom of the pineapple off.
Trim the outside skin off the pineapple carefully.
Use a potato peeler to remove any of the hard eyes.
Cut the pineapple in half lengthwise and then in half again.
Use your knife to cut out the core of the pineapple.
Dice the pineapple into chunks and freeze them (at least 6 hours or overnight).
Dice your banana and freeze those pieces as well.
Place your frozen pineapple, banana, coconut milk and lime into a blender.
Blend until smooth
This will make a smoothie consistency Dole whip, if you want it pipe-able then you can add this mixture to an ice cream machine as I did with my Bosch ice cream bowl attachment.
Or you place the mixture onto a sheet pan and freeze it for 15 minutes, mix with a whisk and freeze again. Keep doing this until it's thick enough to pipe.