Lloyd,
Two weeks is a short term rental, so you will need to get a vacation rental. Check the Rolodex on this website, and the individual pages for each travel spot for suggested hotels and resorts. January is the high season so all rentals will be higher than in the summer and resorts fill up quickly.
The June Monthly Belize Insider newsletter lists property management firms in each expat area. So when you plan for a real long-term rental, of more than one month, this is where you will find suggestions of who to contact in each expat region.