You are legally allowed to bring 1 liter per person, but as a practical matter if you have an extra bottle or two usually the customs official doesn't say anything. You can bring in more but they can charge duty.
For further information on customs click the links below:
Duty-free allowances for visitors entering Belize include 1 liter of liquor and one carton of cigarettes per person. Customs officials may confiscate beer, including beer from Guatemala or Mexico, as Belize protects its domestic brewing industry. The exception is beer from countries in CARICOM, of which Belize is a member. When arriving by international air at Philip Goldson International Airport you can buy up to four bottles of spirits or wine at the duty-free shop in the arrival terminal near the baggage claim area. These won’t be counted toward your regular import allowance.