You can bring in two bottles of wine per person (over age 18), though as a practical matter any reasonable amount of wine or booze for personal consumption is usually okay. Beer is a different matter, because imports of beer are prohibited under law to protect the local Bowen monopoly and to get local taxes. That's why the excellent Mexican and Guatemalan beers are not widely available in Belize.
But as others have noted, Wine Devine (which moved last year to a new location) has a decent selection at prices that are maybe 25% or 30% more than you'd pay in the U.S. And there's a pretty good wine store in Belize City. I'd only bother to bring in wine if there are vintages you especially like.
Belize has truly excellent and inexpensive (US$5 to $7 a bottle) local rums. My preference is Duurley's, a gold rum from Traveller's, but a lot of people like One Barrel. Caribbean white is pretty good, too, if you like white rums. Many imported liquors are available in local grocery stores, at prices maybe 50% higher than typical U.S. prices. Belize has local vodkas and other booze, but it's pretty awful, though cheap.
When you go back to the U.S., you can effectively take as many bottles of rum as you like, as U.S. customs rarely bother with charging duty on the excess for personal consumption. Last week I took back six bottles of Duurley's that I bought at one of the duty free shops at the airport, for Us$4 a bottle.