I went to Paradise Beach on my last trip to Cozumel, about 3 weeks ago now. As stated, it is a nice beach. No entry fee, as the impression is you'll spend money while you're there. Lounge chair use is $2.00, and for $12.00, you can use their aqua park, snorkel equipment, and floating beach mats. US dollars are accepted there, as most everybody there is on one of the cruise ships in port.
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)