bigalc

I completely understand your wanting a beagle. We have three grown ones and a puppy. They are wonderful family and companion dogs, as well as good hunting dogs. They are bred to be trail dogs, and I am sure you could train one to trail coons. The biggest downfall they would have is that they are not bred to have the treeing instinct, so they might follow the coon to the tree, and then go silent. You wouldn't know where they were unless you used a tracking collar. Youcould try training one with a coonhound, and this might help one learn to bark on the tree.
As to what Wheelie said, it is best to train a dog to specialize on one type of game. BUT, with a smart dog and a lot of patient training you can probably have a dog that is competent on more than one kind of animal.