Obviously first, eliminate any medical issues... yadda yadda... :)
But to fix it, know where the problem starts. Cantering on the right lead starts from the left hind, called the "strike off" leg. Most times a problem with a lead comes from a weak hind leg. You can palpate the hip and stifle areas (or have someone show you how) and check for signs of soreness or tenderness.
Also a good exercise is to move the hind quarters around, each directions, before picking up the canter. trot a circle to the LEFT, and really work on pressing yours horse off of your inside leg. Use your inside leg slightly behind the girth, and sit tall and back, encouraging the LEFT hind leg to track underneath instead of slightly to the inside. Also do some leg yeilds off your left leg, which will really loosen up the hind leg.
When you ask for the canter to the RIGHT... start out on a trot circle to the left (do the same as described above when trotting left). HALT. Use your LEFT leg, and ask for a turn on the forehand. (horses hiney will spin to the outside of the circle you just made). From the HALT (or if not possible, ask your horses for just a FEW walk steps first) cue the canter with your left leg aid slightly behind the girth.
The idea is that you have the horse moving off that leg which becomes the canter aid, so he is already responsive to it. He has also loosened up that hind leg and can more easily pick up the lead.
Also do not overbend him in either direction, rather keep him pretty straight while you ask. Sit and slide your inside hip to your outside rein, so to speak, so that you are not riding on the inside shoulder (which also needs to be freed up in order to take the lead.
good luck :)
"The white horse moved like a dancer, which is not surprising: a horse is a beautiful animal, but it is perhaps most remarkable because it moves as if it always hears music."