Preheat the oven to 350°F (175°C). Line a cupcake tin with paper liners. In a blender or food processor, puree fresh watermelon until smooth, then strain to remove excess pulp if desired.
Cream softened butter and sugar together in a mixing bowl using a rubber spatula or hand mixer until light and fluffy, about 2-3 minutes, pressing against the sides of the bowl to monitor texture.
Add eggs one at a time to the creamed mixture, beating well after each addition. Mix in vanilla extract. The mixture should appear smooth and slightly thickened.
In a separate dry bowl, whisk together flour, baking powder, baking soda, and salt. Gradually fold these dry ingredients into the wet mixture, alternating with watermelon puree, starting and ending with the dry ingredients. Mix just until combined.
Spoon the batter evenly into the cupcake liners, filling each about two-thirds full. Place the tray in the oven and bake for 20 minutes, or until a toothpick inserted into the center comes out clean. You should see a slight dome and golden edges when done.
Remove cupcakes from oven and allow to cool in the pan for 5 minutes. Then transfer to a wire rack and cool completely before frosting or serving.
