Check around with the local gun clubs.
If you're not familiar with any, try the sanctioning bodies web sites for clubs that hold their kind of matches.
Like IDPA, USPSA, Steel Challenge, Silhouette, Cowboy, 3Gun, Skeet, Trap, Sporting Clays, and others.
Most local clubs hold a variety of types of matches.
There's a good chance a local club that holds any of the above matches will also have those of the type you seek.