There are isometric exercises that are great for strengthening, and should be safe for your knees. I recognize most of the exercises listed here, since I recently went through physical therapy. My condition was a back injury, but I also have weak knees.
http://www.med.umich.edu/1libr/sma/sma_jumpersk_rex.htm

Check out the wall squat. There's another one where you stand with your back against the wall. With your back straight, lower down into a squat (not quite 90 degrees) with the wall supporting your back. Try to hold it for 30 seconds. It's a real exercise for the quads, but doesn't require moving up and down. The goal is to do 3 of these, then try to get up to a minute or more.