Above all, be positive. There's nothing worse than a parent yelling at a child for not performing up to expectations. Remember that climbing is a terrific life-long sport, so there's no reason to rush things. If the kid's had enough, go out for ice cream and a debriefing of the day's bravery and glory. Give your child a taste of that camaraderie by spending some time after climbing talking about routes and moves.
Many parents find that it is easier to climb with their children after a couple of formal lessons.
You can sign your children up for a course by themselves, or take a course together. The indoor-wall environment is less intimidating for children, but don't discount outdoor programs.