Disney Answer: Expensive!
Located on Disney private island, Castaway Cay, Disney has built 24 cabanas that are available for rent. These are daily rentals that give you access to your private cabana for your day on Castaway Cay. Each cabana features cushioned chairs, chaise lounges, a fridge, lockable storage unit and a fresh water shower. You also receive non-stop non-alcoholic beverages, fruit and other snacks, suntan lotion and fluffy towels. You can also order other cold beverages right from your cabana and have them charged to your stateroom. 20 of the cabanas are located on the far side of the family beach, while 4 of them are located on Serenity Bay (adult only).
Currently, the cabanas are $549 plus tax for the family beach cabanas that fit 6 ($50 more between April 22 and September 24, 2017). For the smaller 4 person cabanas on Serenity Bay, they run $399 plus tax for the day.
Please note, the cabanas are nearly impossible to book, even though there are 24 of them. On most Disney Cruises, the cabanas are booked up right around the time platinum Castaway Club members can check in, which is 120 days before the ship sails. So, unless you are a platinum member, or you are staying in concierge, it is very unlikely that you will be able to book a cabana. However, it is worth trying as soon as you can check-in online, and remember to check back frequently, guests do cancel their cabana reservations from time to time.