The NSRA and Regional small bore associations run LSR leagues in which you can use air rifle up to and including .22
It is however a Sporting Rifle Competition and not a Target Rifle Competition
The distance is 20 yards using the old 25m (PL)free pistol target.
However, there are limitations on the air rifle/rimfire rifle used
They must NOT be purpose made target rifles and there are maximum weight limits, that include the scope and glove (4.5Kgm)
Trigger pressure MUST exceed 500grm
Adjustable palm rests are not allowed. Shooting jackets/shooting trousers/ shooting boots are not allowed
10 metre recoiless air rifles are not allowed as they were not manufactured as sporting rifles and they also usually exceed the max. weight allowed
I hope this helps
For a full set of rules e-mail the NSRA Competitions Dept
John