Keep your shots to 75yrds or less. A .22lr doesn' t pack much punch, so you aren' t going to be able to penetrate the shoulder. What I usually do (mind you I have a very accurate Marlin 60--->2MOA @100yrds) is take head shots or take quartering away shots placed just behind the rib cage. The head is obvious, but the rear rib shot is important too, from side-on, you can' t penetrate to get to the heart through the muscles surrounding the shoulder, so you need to get through the ribcage where things are thinner, but to do this well you need to damage a couple key things, i.e. heart, lungs, diaphram. If you hit in the rib cage, it' s probable that you' ll hit the lungs if not the heart, but they can run a long ways on one bad lung or two bad lobes (since back there you are penetrating the lower lobes of the lungs and " panic breathing" depends on the upper lobes). If you take a quartering away shot on them, you puncture the diaphram on the way into the lung, they breath hard and the diaphram shreds itself, plus you get the lung and a more likely hit on the heart.

How fast can you fire your 10/22? I' ve never had much luck with rapid firing them, but I am able to bump fire my Marlin fast enough to hit a can twice (if not three times) before it falls off a fence, so I' ll oft bump fire it into the ribs of coyotes just for extra insurance.

You might consider stepping up to a .22mag or hornet, for the extra umph in a light arm.

Best bet, however, is to step into the world of high power varminting, buy a .223 (as much as I hate .223' s they' re cheap) or a .22-250. It will cost you more, but I guarantee you' re costing yourself yotes by using a .22lr, you don' t have the range. I don' t have a .22-250 anymore, but I' m buying one again soon, but I' ve been using my .30-06 and my SKS a lot this year, even with the pathetic trajectory of the 7.62x39mm round I have AT LEAST twice the effective range over the .22lr' s I own. Any deer rifle will be better than a .22lr, I use my .45-70' s before I take my .22' s out anymore.