Check out this link. It's for a trash can carrier rig that fits into a receiver hitch. A buddy of mine uses one of these since he has a very long driveway (0.2 mile), and it works really well. It's spendy, but it is well built and does the job, and can even haul two cans. It also has a version that works with an ATV, so they may already have a version that could mount to a tractor. If not, you could probably make one work with only a little bit of effort.
http://cansporter.com/
One thing you will need to consider is how much weight your cans typically weigh when full. I carry mine by hand, but if you fill a larger rolling can, you may have a LOT of weight there. If so, can you pick that much up with your tractor without tipping it up? If you only have one can, and the weight is within the capacity of a tractor's rear hitch, you should be able to fab up a bracket to pick up the can. You also have to get it high enough that the can doesn't contact the ground when you cross over any angle transitions.
Another thought that comes to mind would be making some sort of low cart, with better wheels, a nearly vertical post to strap the cans to, and a drawbar to pull it with behind the tractor. It wouldn't be nearly as maneuverable, but still would work and would be simpler to fab. I can even picture a way to make it out of wood.
I'd say that's enough brainstorming for one evening. I'll shut up now and give others a chance to chime in.