There are lockers for rent on Coco Cay by the snorkel shack. But I don't think they were yours for the day where you could come and go to them to get stuff or put other stuff in them. It was more of a "one time use" deal unless you paid again.
Since Coco Cay is a private island, the only people there are RCI staff and the other passengers. In other words the probability of something being stolen is the same as aboard the ship.