I would not take my own gear, too much to lug off and back on the ship. Two sets shared will be fine I am guessing, I saw some families doing that both times I was there. I think it is like $26 or something, I can't remember, but you can book online easily and your "tickets" will be delivered to your stateroom Sunday night (you will find them after dinner).
Caution, too, it is a little rocky in the shallow water of CoCo Cay, so if you can, take and use sand shoes.
Have a grea time! The island is lovely. The "main beach" is great but walk all around and you will find more beaches and nice shaded areas to lougnge about at.
Sovereign of the Seas 12/22/02
Sovereign of the Seas 04/27/03