Over the past 18 years, I've had good experiences with Budget, Avis and Crystal, among others. In fact, I've rarely had a bad experience with any rental company.
On the Sunday closings, most agencies will arrange to be open on Sunday if you schedule your pick up or drop off it in advance, or in the case of companies with locations at the international airport and in Belize City, one is usually open, and the company will take you to the other location (or other destination in the area) if necessary.
--Lan Sluder