Cheap means different things to different people. In Corozal, nothing is really expensive (US$65 is about the top end, except at one rather odd place) but then there aren't a lot of really cheap places either. Central Guesthouse, on I think 6th Avenue, would be one fairly cheap, safe place -- haven't checked lately but it was in the US$12-$14 a night range. A step up would be a place like Marvirton Guest House, probably US$20 to $25.
--Lan Sluder