Gallon Jug coffee (to which Bill refers) is pretty good. Bowen is the only commercial producer of coffee in Belize -- his farm manager brought the plants in from Costa Rica. But it's not as good as Costa Rica or Guatemala coffee because it's grown at a lower elevation.
I second Cafe Ole as having good coffee, but some of the other San Pedro hotels and restaurants have okay coffee. On the mainland, especially around San Ignacio, the better places serve good Guatemalan coffee, and a few lodges, Blancaneaux, Hidden Valley and Chan Chich (at Gallon Jug) grow and roast their own coffee.
Used to be in Belize, and at some place it's still the case, all you can get is instant. 'Course, it wasn't that long ago that even at the best hotels in Belize the "juice" at breakfast was Tang.
Things have really changed for the better in the past eight or ten years.