Offered in no particular order:
http://www.cayemanagement.com/http://www.ambergrisvacationrentals.com/?page_id=50//ambergriscaye.com/m-m/index.html
//ambergriscaye.com/blease/index.html
Also, you could just get a hotel for a few days, connect with people, start to read the local papers, meet with Caye Management, M&M Rentals, etc., and see what's available.
Or you can look on this message board here:
//ambergriscaye.com/forum/ubbthreads.php/forums/5/1/Classifieds.html
I believe there have been a couple of places advertised lately.