Since I've noticed this has come up before I found this info on worldtravelguide.net it has some other info also such as passport info/departure tax/general info etc...

Duty Free

The following goods may be taken into Belize without incurring customs duty:
200 cigarettes or 50 cigars or 250g of tobacco; 568ml of alcoholic beverages; 1 bottle of perfume for personal use.