I know what it is. A petite caliber from the early Cooper days. Before the 17m2 and 17hmr came out. Sort of a necked down .32 acp case. Ammo or brass might be an issue, but there must be a member here who knows more about the situation than I do.

 

Sort of a necked down .32 acp case.

I think you may be thinking of the TCM brass. The 17 CCM and 22 CCM (Cooper Centerfire Magnum) are both based on what is basically (very similar) a 22 Win. Mag. case size, but in centerfire using a .224" bullet in the 22 CCM.
Those are very nice rifles, hope you (mrmit) got it for a good price, given the ammo situation.

22 ccm brass - Google Search

New-To-Me Cooper .22 CCM - Saubier.com

New-To-Me Cooper .22 CCM Small Caliber Discussion Board

www.saubier.com

P.S. Brass may be pretty hard to come by. It can be made on a lathe to the 22 CCM spec. as a 'parent' case and necked down to 17 CCM. Did you get a set of dies with the gun? If not, CH/4D has them: Caliber List : CH4D

P.P.S. Edit: Just saw your #4 post....good deal on getting the ammo and brass and dies. As long as you keep loads reasonable, your supplies should keep you shooting for a good while, congrats on the purchase!

 

These two sites might be your only hope. If you conquer the ammo problem you should have a fun rifle.
Reeds Brass

And for load info
saubier.com

 

Managed to get 200 rounds of loaded ammo and 200 rds of brass along with a set of dies with rifle. Just concerned that life expectation of the brass may not be too good. Congratulations on knowing what it was.

 

I sold a set of the cooper ccm couple years back. Had factory cooper brass for both. Noted on the 17 ccm brass not to be reloaded. Disappointing
good luck

 

I sold a set of the cooper ccm couple years back. Had factory cooper brass for both. Noted on the 17 ccm brass not to be reloaded. Disappointing
good luck

That was only the original factory brass that was lathe turned. After that, Fiocchi made two runs of fine brass, Shcroeder also made brass modified from hornet brass.
Brass is tuff, go the Small caliber forum and post an add.
Great little caliber, I get 3200 fps. With 9.2 gr of 1680 and 20gr Bergers.