Hi!
There is liquor for sale at the airport when you arrive. It's duty free, so not a bad deal. Most everything is available. As for liqour stores on the island, I really don't recall any specifically, but think you can get rum and the more popular liquors at the large grocery store. Ambergris has a beer distributorship and you can buy the local, Belikin Beer, there by the case. It's much cheaper that way. If you have a fridge at your accomodations........ Belikin Beer seems to be the most popular, but there are a couple other brands. If you like a dark stout beer, like Guiness, Belikin has a WONDERFUL dark stout that will knock your socks off!!!