Put the gelatin in a medium bowl. Whisk in 2 cups boiling water until the gelatin is fully dissolved. Cool the mixture to room temperature and then whisk in the coconut milk and rum. Pour the mixture into a 13-by-9-inch baking dish. The coconut milk solids will rise to the top to make a skin. Refrigerate overnight.
Dip the pan in warm (not hot) water for 15 seconds to loosen the gelatin. Use the cookie cutter to cut out pineapple shapes. Gently lift them out of the pan and onto a plate or baking sheet.
Mix 3 or 4 drops of green food coloring with about 1 tablespoon water. Dip a piece of paper towel in the food coloring and gently dab the "leaves" of the pineapple shapes to die them light green. Refrigerate again to dry the food coloring, about 30 minutes; serve.