Pour the tropical juice and coconut milk into separate ice cube trays and freeze. Peel the banana, cut into chunks and freeze on a plate.
When you're ready to make the drinks, add the frozen juice and coconut milk cubes to a blender with the banana chunks. Add the pineapple, rum and mango and blend on high until very smooth, light and creamy, scraping down the sides of the blender several times, 1 to 2 minutes. Immediately pour (or pipe for a soft-serve look) into 4 glasses. Garnish with mango chunks and maraschino cherries and serve.