The end of Sept could be a bit late for CO, but you could hit it lucky and see some good weather.
re private campgrounds: A good one in Torrey UT is called 1000 Lakes. It is a couple miles from Capital Reef N Park. If you aren't bothered by mountain roads, take 12 from Torrey south when you're headed to Bryce Canyon Park.
If you're going through CO from UT on 1-70, take 50 south from Grand Junction and then east to Pueblo, etc.
a decent rv park called Heart of the Rockies is about 10 miles west of Salida, CO on 50.
These are not resort type rv parks.