Using a sharp knife, carefully scoop out the flesh of the watermelon and cut it into cubes, removing and discarding as many seeds as possible.
Place the watermelon cubes in a medium sized mixing bowl and gently combine them with the banana slices.
Set aside.
In a small bowl, combine the lemon and lime juice with the rum.
Add the 2 ounces [1/4 cup] of sugar and stir the mixture until the sugar has dissolved.
Spoon the watermelon and banana mixture into the melon halves and pour the rum mixture equally over the two halves.
Place the melon in the refrigerator to chill for 30 minutes or until ready to serve.
Remove the melon from the refrigerator and place the halves on a serving dish.
Sprinkle over the remaining 2 tablespoons of sugar and serve immediately.