This doesn't answer your question since I really don't know so forgive me, but I do offer an alternative. ATMs (called ABMs in Jamaica) can be found just about as commonly as they can in the States. There is one in the game room/internet lounge at CSS for sure, not positive about the other resorts. If you are out in town, look for the Red Scotiaback machines to avoid high fees you'll end up paying at places like Island Village/Margaritaville. I carry an ATM card tied to a bank account with $500 in it so if the card gets somehow stolen and compromised, I'm only out that much. I can move money into that account by calling my bank or make a transfer over the internet if for some reason I need more.
Why do you need Traveler's Checks, Maryanne? You will only need cash for spa tips and anything you purchase from the vendors. We take a few hundred dollars every time we go, and come home with cash. If you DO take cash to buy from vendors, take an assortment of small bills.