Parasailing is one of those things that I think cruise ships consider inherently dangerous. I have never seen a ship's sponsored excursion offering it.
There may be other places to do this , but I can tell you one. Cable Beach. Easy to get to by cab or bus. The beach is public (even by the hotels). Vendors do parasailing and jet skiis. I would be guessing, but I would imagine the same is true for the beaches off Paradise Island.