If its available in your area, while I would not name it the same as you... I would just call it an club by another name as to not attract the attention of the yahoos that like to complain about everything.
It could do the hobby some good, especially if you get enough members for a filling apparatus. Just watch the insurance and air quality regulations for ranges etc. We almost had funding to start an indoor range but lost it before the zoning battle. But that was for powder burners, not air guns. The news gets people all scared about anything related or looking the same.
In WI an airgun is considered a dangerous weapon (Which is kind of wierd considering folks can have a lot of different tools just as dangerous) so you may have similar legislation in other areas inhibiting your clubs members. In wisconsin it is a no no... even if your on a TRO. No red rider for your kid.
As far as the powder burners goes... It may not be up to them. I know the local laws for firearms say if I was driving you to get a burger and if your at my house, but at a range... The articulation of possession can be varied based on laws on all levels of jurisdiction. So... they act in a manner so no one will get in trouble if someone with a felony conviction is there. While its Definitely not pleasant for you. They are not singling you out specifically in some cases at least.
I hope you find a solution.
The same goes for Airguns and archery. I do know that some states will not allow a felon to possess anything capable of shooting a projectile but others have no such restrictions.
I am not too sure that I would go out and advertise a club strictly for felons. That seems to run against the goal of entering the whole of society as a productive and responsible citizen. I think that I would start a club and have as one of it’s charters that any person who can legally possess an airgun is qualified to join. Maybe the non-felon members would gain an education or experience that could change their minds and attitudes about people with a record.
Would be a double win for people with a record.