The dictionary (English or American) is of no help when it comes to local pronunciations. Am-ber-gree is how whale vomit is pronounced in polite French-American company, not how it is pronounced in Belize.
Belizeans usually pronounce it Am-BUR-gris or sometimes Am-BUR-jess. The accent is always (almost always) on the second syllable.
Or you could just say San Pedro.