Doing alot of transitions is what helps, most of the time. You really have to build up the muscles, especially for them to hold a canter on a circle. The more you can do it off line, in a large round pen, I think, is the easiest, as there is no interference from a line, or a rider. Just do a lot of transitions, walk-trot-canter, canter-trot, walk-trot-walk, trot-canter, etc...over and over and over again, until the horse canters full circles without issue.
And when you are working undersaddle, try to drop them back down to the trot BEFORE they do it on their own...if you know she is going to break in the corner, then drop back down before you get to the corner, and after the corner, bring her back up to the canter, before corner, drop back down, etc...eventually you will try to round one corner, before dropping her back down to the trot before the next corner...Try to stay out of her mouth when teaching her to carry herself...the less you're pulling on her, the less she'll have to lean on, and possibly pull herself off balance. I do alot of coasting in the arena with horses that need to learn self carriage as well. Put horse in a gait, and stay out of their way unless they break gait. Just drop the reins, and let them figure out how to carry themselves with as little interferance as you can.
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."