There are irons, washers, dryers, and ironing boards on the Paradise. You'll find laundries on most of the lower passenger decks. You'll want to go early in the morning (8:00 am or so) or right before it closes in the evening (I'm not sure when that is).
Be sure to bring your own can of starch and get it before you get to Miami because you won't find anything near the port to get it. We took two cans of Faultless and wound up leaving one for the next bunch of folks.
The Paradise is a great ship. If you have any questions, feel free to email me at firstname.lastname@example.org