Rccl does not have a passenger laundry - I've only encountered one on HAL. Try bringing some wrinkle release spray - works like a charm. Otherwise, you can have the ship's laundry service press your things at a relatively reasonable rate.
Carnival will press them for you if you like. I cannot remember the exact prices but I had to have a couple things laundered and the prices were not all that unreasonable, certainly more than your local cleaners but not enough to be considered gouging.