Have you ever tryed a legg press and leg extension? How did that work for you?
Swimming is great, and low impact cycling (don't go nuts on the bike).
Hi! I have problems with my knees also and have to watch what I do. I have discovered I can do squats as long as I don't bend my knees over 45 degrees and I just stay in that position (no moving up and down).
I have no answer for jumping - it's just not going to happen with my knees/body. I do have a stationary bike -
much better than a treadmill.
If all these are impossible to do. I am starting to think there is no real replacement. Cycling or swimming really has nothing to do with strenght training ( not that they are bad for the legs, just something completely different )
I know it's a little old school, but what about step ups. If the steps are not steep, it may not be such an issue. Plus going up and down stairs is a killer leg workout even if you walk it. Be mindful of the impact. Just an idea.
Cycling is for you! Way more fun than squats, lunges, or leg presses anyway! (I am shamelessly biased)