On the eastern, your first call will be at St. Maarten. There's a store at the base of the pier that sells beer, wine, etc., which is convenient to get supplies for the ship. I don't specifically remember them having N/A beer, but they probably would. They had a fairly large selection. I'd take a look there when you first get off the ship. If they don't have what you need, I'm sure you'll be able to find it in downtown Philipsburg.
Many of the bars on board serve the O'Douls, or Miller Sharp's, I think.