This is roughly what I put in, but I messed around with it a few times.
4 cups of watermelon - cubed and frozen
1/2 cup rum
1/4 cup orange liqueur
1/4 cup fresh lime juice
Add watermelon and liquids to a blender. Mix until smooth. Add ice to bring volume back up to top of blender. Mix again. Taste and adjust until you get the ingredients right.
I had no orange liqueur, so I tried orange vodka. That really didn't bring enough sweetness, so I used more simple syrup than you might normally need. Another option would be to try orange juice.
The other idea I would try is to use watermelon flavored rum, which could enhance the flavor and sweetness.