I was a 4H rifle/pistol coach about 15 years ago when the kids were younger (three generations of 4H in our family). It's a good program. A first step would be to contact your state 4H organization. They can steer you to local clubs or county federations of clubs that are active in the shooting sports. They're always looking for adult involvement. 4H isn't just for farm kids, and it isn't limited to agricultural projects.
Another way to promote the shooting sports is to become a volunteer firearm safety instructor (you know - that class people have to take to get a hunting license). Contact your state department of natural resources for more information and upcoming instructor training. You don't even have to teach the class. I know a couple of people that just took the training to be more effective with their own children.