In the eastern Caribbean, local currency is preferred, although US dollars are generally accepted. Change will be in local currency. I've never seen anyone use credit cards, and as far as I know, US checks are not going to be accepted anywhere for anything.
That's better than US customs. They want the exact amount and won't take anything else. I think my last fee was $23. They wouldn't take $25 even when I said put the two bucks in some charity box. I knew better than to say put it in the coffee fund. Had to walk to a bank and get change.