Stir together the mango nectar and lime juice in a large measuring cup. Stir together the pineapple juice and grenadine in another large measuring cup. Stir 3 tablespoons rum into each of the juices, if using.
Pour the pineapple juice into twelve 3-ounce paper cups.
Holding a spoon, rounded-side-up, just above the surface of the pineapple juice, very slowly pour the mango juice over the spoon so that two distinct layers are maintained. (Note: If you are using rum, you will have more of a tie-dyed effect.)
Freeze the cups until icy, about 2 hours. Insert the ice pop sticks and freeze until solid, about 3 hours more. Remove the pops by tearing off the paper cups, and serve.