Chris_B is on to something...
I tried again with the AR. I could not do it no matter how hard I pulled the rifle into my shoulder with my right hand. I could keep the stock from falling off my shoulder, but there is no way the sights would stay "on target"
However, I can keep my Winchester Model 12 shot gun on my shoulder, holding it with just my right hand. I notice that the stance for a shotgun puts my right elbow well underneath the stock, and my body is only slightly bladed to the target. I am also crouched.
With the rifle (any rifle) I am fully errect, most of my weight is on my right foot, and bladed 45 degrees or more to the target. Left elbow directly under the forearm, and right elbow 90 degrees out (horizontal). I notice that I am fully supporting the weight of the rifle with my left hand, and my right hand is relaxed and pulling into my shoulder just enough to maintain shoulder contact. I don't think about it, this is how I have always shot a rifle, it is how I was taught.
If I pull my right elbow under the weapon, and hold it more like a shotgun, there is no problem supporting it with just my right hand. But that does not seem like a very accurate way to shoot...
Supporting the firearm from underneath is going to be easier than supporting it from the horizontal.
An "elbows in" stance is taught by a lot of mil/leo instructors. Keeping your elbows in provides a narrower stance so you don't bump into things as easily, and you present a slightly smaller target. If you slightly crank down on the rifle like twisting a towel to wring it out, you might get a little more stability. It probably won't be as stable as the traditional olympic/competition stance, but it shouldn't be a whole lot less.