They accept ONLY credit cards. They have stopped accepting cash (I beleive according to a recent post by Randymon).
Two things to beware of:
1) Call your credit card company before you go and let them know you will be traveling to Jamaica. My card was refused at the Tour Desk and it was a mess trying to straighten it out from Jamaica.
2) The credit card fee is imposed by your credit card company and not the resort or even your bank. My bank (the one who issued the card to me) was unable to get the credit card company to reverse the 2% "Fraud Fee" that they charged. From what I have read on the message board, Discover may be the only credit card company that does not charge some sort of foreign transaction fee.
We used a CC at the tour desk to book a tour to Mystic Mountain. No fee. You would probably get one from your CC company if they impose a fee for transactions in a foreign country but you will get that anywhere you use that particular card in Jamaica (ours didn't). No fee from the hotel/tour desk and the charge is in US$.