Try the belizeforum.com Do a search an CC accomodations. You'll get so much info your head will spin! Also, belizefirst.com Lan Sluder is a well-known writer and magazine publisher. He does "top" lists on many categories, including lodging.
As for discounts for longer term stays- you can always try. Depends on how full the place is, or maybe the mood the owner is in, or who knows? I emailed several places asking for a monthly rate. All I got was quotes on daily or sometimes, weekly. The bargaining has to be done in person.
Pick a place and pay for a day or two, then spend some time looking at the rooms and negotiating if you like it. You'll see the island and meet some neat folks. Many ex-pats and a few Belizeans. If you like sev'l places, think about supporting Belizean owned businesses. Yes, I know, Belizeans work at the non-BZE owned businesses. But it's really not the same. No, I have nothing against ex-pats-who knows, I might BE one someday- but those folks will make their nut anyway. When you support BZE businesses, you often help an extended family. And put the lie of lazy Belizeans to rest.
You'll have a great time, I believe, wherever you end up. Just don't pay up front for an extended period until you see the room. Safest method to assure you'll be happy. Happy trails!