Like the PP said, there is an abundance of free shade on the island. We did not visit the water park, but there are many, many palm trees on the beaches, and lots of options for shelter.
On CoCo Cay there are LOTS of beach chairs. I just dragged one under a tree and created my own little oasis. It was perfect. Just find a beach with some trees near it. There are umbrellas, but they aren't allowed on all of the beaches.
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