Hello iliffwfms, and welcome to cruise-chat; since Half-Moon Cay is Carnival's private island, I would imagine U.S. dollars would be fine. You can probably even charge to your shipboard account.
I haven't been to a lot of Caribbean ports, but every one I have been to took U.S. dollars.
I haven't been to Half Moon Cay yet. The prices will be in US dollars. My understanding is, and as f-mattox mentioned, you can use your shipboard account on Half Moon Cay.
Does anyone know if the Half Moon Cay bars/shops accept cash at all?