The most suitable time to go to Belize is the dry season, which occurs between late November and mid-April. The season has sunny days, calm waters and excellent diving, snorkeling, and Mayan ruins exploration conditions. It is the height of the tourist season, too, and hence it will be more crowded and the prices should be higher.
Working on a smaller budget and with fewer people? The shoulder months May or early November, are the times you should choose, though you may need to deal with rain at times. The months to avoid are June to October, when it is the hurricane season and extremely humid.