What about cabana rebtals by the ship's pool. Is it Celebrity or Princess that charges something like $25/day for a private cabana? You don't even get the sun, and how private is it anyway?
Princess has the Sertenity area at the rear of the ship for $10 half day or $20 all day. Personally, I think they are a rip, unless you have an inside cabin, you can enjoy privacy right on your own balcony.