You should be able to use your SeaPass card seeing as how this is Royal Caribbean's private island. You can reserve your Beach Mat at the Shore Excursions (or Explorations) desk on the ship or when you book your cruise. They are $10 and are available at your leisure for the duration of your stay on the island.
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)