Chip's response is excellent. Look on AAFTA.org. They shoot Field Target. Airgun silhouette matches are listed in the coming events on the NRA website if they are NRA approved matches. If you are interested in silhouette try steelchickens.com. They have a section on airguns. Many clubs and the clubs I shoot at are not only airgun clubs but rather general shooting clubs that have airgun programs so you can check with your state shooting association and they generally list member clubs.
If you get on any of the forums, like this one, and ask about clubs in your area you usually will get a response. I certainly never pass up a chance to promote airgun shooting and my clubs in particular( I belong to several). There are several clubs in the Philadelphia, PA area that have some kind of airgun activity. My asscoiates and I run matches at Falls Twsp. Rifle and Pistol Assn. and there are also matches at Delaware County Field and Stream Assn. If you are near us check out the websites.
If there is nothing near you then I suggest you get into a local gun club and try to promote it. lots of people are already airgun shooters and you may get a few of them to participate.
Sorry for the long response but I get wound up about shooting!
