Yes — watermelon is hydrating and completely safe for parrots, seeds included.
Keeper's noteGreat on hot days. Very wet droppings for a few hours afterward are normal — it's the water content, not illness.
Why watermelon is good for parrots
Watermelon is over 90% water, making it a perfect hot-weather food, and unlike apple seeds, watermelon seeds contain no cyanogenic compounds — many parrots enjoy the seeds most of all. The rind is safe too if well washed, though most birds ignore it.
How to serve it
Serve chunks with or without seeds — both are safe.
Chill it in summer; offer on a skewer or in a bowl.