To encourage young riders to trot or canter on a horse, you should start by giving them lessons on the lounge line. Always start with the trot and put them on a reliable mount that is not easily spooked. Let the child hold on to the horn or pommel of the saddle to balance them and gradually have them remove their hands. See if they will spread their arms out for balance and remind them to sit tall and deep in the saddle. Eventually you should be able to move on to the canter. If the child is really hesitant about it you can trot the horse in hand. Always remember to be patient with young riders and praise them when they have done well. Don't forget to be reassuring because it can be frightening at first.