No, this isn't really a Paloma. It's missing the one key ingredient (grapefruit) that distinguishes a Paloma from most other tequila cocktails -- and instead calls on watermelon, that quintessential American summer treat, to do fruit duty. —Merrill Stubbs
To make the watermelon juice, put half the watermelon cubes in a blender and blend until liquid. Set a fine mesh strainer over a large bowl and pour the watermelon juice into the strainer, gently stirring with a wooden spoon to coax the juice through the strainer.
Discard any pulp in the strainer and then blend and strain the rest of the watermelon cubes. Cover and chill the juice until you're ready to use it.
To make the drink, put 4 or 5 ice cubes in a tall glass. Add the tequila, 1/4 cup watermelon juice and lime juice and stir gently. Top with club soda and stir briefly. (Use these same proportions to whip up an entire pitcher of Palomas.)