Do these exist?  I'd be interested in one as a break barrel system.

Never had an air gun, no nfa requirements right?

I just noticed you mentioned break barrels...

Break barrels AKA springers. Never seen them that short and I'm sure it would be a pain in the ass to cock.

Air guns are not currently classified as firearms under the GCA or NFA - some individual states have classified them either as firearms or deadly weapons, though.

There have been several short barreled spring airguns, 10" or so barrel length, but they have to have some sort of extension to make them manageable to cock.  

When you get to PCP airguns, there are a host of bull pups, and true carbines with short barrels.  Of the more accurate (precise) bull pups that come to mind are the Cricket, and FX Impact.  But, beware the sticker shock will be surprising.  

The other thing about many of these PCP airguns is that they come equipped with built on silencers.  It makes them very quiet to shoot providing you do not try to push the velocity above 900 ft/s.  Pellets, generally don't like to go that fast anyway.

Take a look at the Kalibrgun Compact Cricket and the Short Taipan Mutant.   A picture of my my Compact Cricket is on the 2nd page of the Airgun Picture thread.  They are ridiculously short carbines but absolute lasers when it comes to accuracy.  I also have an old  .25 BSA Supersport break barrel springer that has about a 10" barrel with an extension, which is more to attach a moderator then a cocking aide but that's how I use it.   It's a hoot to carry but pretty anemic in the power area.   I use it for short range (within 25 yards) rabbits and for shooting pigeons inside barns.

Not sure about a break barrel, but you can build what you want at the Crosman custom shop.It will be a multi pump or co2 though.

http://www.crosman.com/custom-shop/#

Not only does the ATF not regulate airgun length, but they also don't have any jurisdiction over "moderators" on them.  This is the aforementioned Mutant Short.  13.5" CZ barrel with a proprietary moderator.  Thing is super quiet.  I was shooting wasps off of an old birdhouse at 25 yards with it yesterday.  

Is it Crossman that has the spring air pistol that comes w/ a cocking piece extension?

I think you're referring to the Webley Typhoon.



 

Nope.  http://www.crosman.com/airguns/air-pistols/trail-np-break-barrel-pistol-177

This.

You could look at the TX200 HC by Air Arms. It's a carbine version of the TX200 which is arguably the most accurate mass produced spring gun out there. It has an underlever for cocking and I can tell you being the owner of the standard TX200 that you will be hard pressed to find a finer spring gun.