Watermelons are curcubits (relatives of squashes, pumpkins, and gourds), and their seeds are not toxic. It's drupes (fleshy fruits with a central pit, also known as stone fruits) which you want to watch out for. The pits of apples, peaches, cherries, apricots, and similar such fruits contain trace amounts of cyanide; harmless to us, with our larger body size, but they might poison a small bird.
(Almonds are also drupes, by the way, but humans have selectively bred them for low toxicity. Still, I'd be careful about feeding a lot of almonds to a bird in one sitting. Small amounts of almond should be safe, though.)