The man standing beside the stout king will hand you the pearl once you complete his task—matching the right shells to the candidates.
Head to the cave to reach the neighboring village, where you'll find a man tied to a palm tree. Have your way with him, and you'll receive a coconut in return.
Still on that side of the island, near the massage therapist, there's a spot where seagulls flock. You'll find a man standing there—this is where you can catch a seagull.