The locals (and I mean the ones who were born and raised in Belize) told us that as long as you do not carry a bottle, it is okay. They informed us that as long as the beverage is in a cup, all is good with authorities. The only problem that you should keep in mind is that it is virtually impossible to drive with a drink in your hand anyway as the bumps cause you to spill more than you can actually consume. For a short drive, it's not worth it to drink and drive.
Thanks knotborde. I actually already have my 'coffee' cup packed - the insulated kind that has the lid that snaps on. Hopefully that will work. Since we haven't been to AC in 10 years we want to go around and check EVERYTHING out.