The most likely candidate for a black bird with a red throat in the Caribbean is the Lesser Antillean Bullfinch (Loxigilla noctis). The adult male is a striking, sooty-black bird characterized by a distinct rufous-red patch on its throat (chin) and a smaller red spot above the eyes. They are highly successful and "bold" birds, often seen hopping around outdoor cafes or garden terraces in the Virgin Islands and throughout the Lesser Antilles. Another possibility, though less common in gardens, is the Magnificent Frigatebird, which is a large, all-black seabird; during the breeding season, males inflate a massive, vibrant red throat pouch (gular sac) to attract mates. However, if the bird you saw was small and sparrow-like, the Bullfinch is almost certainly the species. They are often confused with the Carib Grackle, but the Grackle is entirely black with yellow eyes and lacks the distinctive red throat markings.