I have a friend in Missouri. Here's what he has listed.
There's a range in Arnold that has regular matches of all types:
http://www.arnoldgunclub.org/
There's a big range in St Louis that has all kinds of matches:
http://www.shootingstl.com/drupal/
There's the 67 Gun Club in Farmington.
http://www.67gunclub.org/
There is or was a range in St Clair:
Indian Trail Gun Club
990 Virginia Mines Rd
Saint Clair, Missouri 63077
The Missouri Department of Conservation has primitive ranges around Missouri.
One is near Cape Girardeau Missouri.
It apparently has shotgun matches, but no rifle or pistol. To find out about shotgun matches, I'd contact the MO dept of Conservation.
I "think" he said the shotgun matches are conducted by a private gun club.