Aerocaribe Airlines flies from Cancun to Belize International direct Thursdays, Saturdays and Sundays. Not cheap but fast.
If you are going to Ambergris, it would be a lot cheaper to fly from Cancun to Chetumal. Cross the border with a tour van or taxi and fly direct from Corozal to AC. Aerocaribe to Chetumal and Tropicair or Maya Airways from Corozal to AC direct.
Aerocaribe web site link is below: http://www.aerocaribe.com/english/Default.htm#