Just returned from there and it seems that there would be wild pig to hunt at the very least.
Belize hunting (http://www.huntingreport.com/worldupdate.cfm?articleid=542)
Here is a little info..
I did some medical training down there.
It was spring and the turkeys were callable just like here. I saw a few pigs in the jungle. Never saw any deer or water buffalo. I did see a few small crocs in a river and jags were rumored in the area. Our guides hunted but we never had the time to talk bowhunting.
There is some world class Bone fishing in Belize but not sure about the hunting.
monkeys
There is a great book called Jungle Hunter by a guy from Minnesota named Cavanangh. He hunted everything down there, DYI. He used a shotgun mostly but still..... Again, great book full of info.
CJ
http://www.booktrail.com/Hunting_AsiaEurope/Jungle%20Hunter%20-%20Big-Game%20Hunting%20in%20South%20America.asp
A link to "Jungle Hunter".
Have been fortunate enough to fish there on a couple of trips.
There should be some great bowfishing there.
Thank you.
Cocobolo!
Lots of whitetail deer and a javalina variant called a white-lipped peccary. There are also good numbers of feral pigs. Great country.