Drain the canned pineapple and mandarin oranges in a colander over the sink for 15 minutes, shaking gently to remove all excess syrup.
Beat the softened cream cheese in a large mixing bowl using a hand mixer on medium speed until completely smooth and airy.
Mix in the dry instant pudding powder until it is fully incorporated into the cream cheese.
Fold the thawed whipped topping gently into the cream cheese mixture using a rubber spatula.
Add the drained pineapple, mandarin oranges, marshmallows, and shredded coconut. Fold until everything is coated.
Slice the bananas, fold them in last, and chill the bowl in the refrigerator for at least 1 hour before serving.