I don't know if this is not something you want to do with a green horse, but one of the things they do at my lesson barn when teaching beginner riders to canter is to get them to go up into two point while trotting and then ask for the canter (in a corner). Apparently the idea is that it can be easier for the horse to pick up the canter if you're up off their back than if you're sitting. (That and it's easier for a rider who may not be comfortable sitting that transition yet).

Might be worth a shot?