JJ, welcome to the thread :)
Canter is something that really needs to be worked on through lunging and saddle work, not stretches and what not on the ground.
Depending on what you mean by green horse (breaker, green broken, green as in older but not done much etc etc), I would be starting with work on the lunge, preferably with side reins or double lunge reins if you know how to long rein. This gives the horse a contact to work into as opposed to lunging willy nilly around with no contact allowing the shoulders to drop and back to hollow.
Lots of transitions between all gaits, and within gaits.
Under saddle, same deal, lots of transitions, especially within gaits which will greatly build up balance and strength behind. Changes of rein, leg yield and shoulder in exercises, circles of varying sizes etc. It will all help the canter.
To introduce the canter to horse that struggle with it a little, I'd use the spiralling exercise that I described earlier. It really helps to establish that basic connection between inside leg and outside rein, the horse is already in correct bend, around the inside leg, so all you need to do is pop your leg back to get the canter which will be nicely set up.