Alma de Mexico Airlines now has regular scheduled flights from Cancun to Chetumal. They fly late down to Chetumal and early up to Cancun, giving plenty of time for same day onward flights.

http://www.alma.com.mx/ing_default.php (English)

It is easy to get to Cancun on holiday charter flights, but also easy to get to Cancun from Mexico city. Mexico city has many international connections, so people coming from Europe now have a way to get to Belize without all the eye scanning, fingerprinting, lack of transit facilities, and just general chaos that having to travel through the USA, when you don't actually want to go there at all, generates.

Couldn't find any seats > July

Or May, tried every day of the week on a one way just in case it was only specific days of the week.

I tried for 2 weeks in June and no flights were offered!!!

same here.

I played with the site and was able to schedule flying from Cancun to Chetumal on 4/18 and return on 4/19 for $970 pesos(I guess) round trip. But I could not get any dates beyond that. Maybe problems with the site?

Great if you are a drug runner....