Game plan: The watermelon lemonade can be made and refrigerated up to 8 hours in advance.
3 pounds seedless watermelon, rind removed and cut into 1-inch cubes (about 6 cups)
1 cuplight rum
1 cup freshly squeezed lemon juice (from about 7 medium lemons)
1/2 cup blackberry or raspberry liqueur
2 tablespoonsgranulated sugar
Blackberries, for garnish
Set a fine-mesh strainer over a large bowl and set it aside.
Place the watermelon in a blender and blend until liquified, about 1 minute. Pour through the strainer into the bowl and scrape a rubber spatula against the inside surface of the strainer to push the juice through until only pulp remains. Discard the pulp. (You should have about 3 cups of juice.)
Transfer the watermelon juice to a nonreactive 2-quart container. Add the rum, lemon juice, liqueur, and sugar and stir until the sugar has dissolved. Cover and refrigerate until chilled, about 2 hours. Just before serving, stir to recombine. Pour over ice and garnish with a few blackberries.