I am trying to picture somebody with limited range of motion in her knees but have a hard time imagining it.
Well, whatever the case may be, the only other alternative is the use of arms. The upper body ergometer has already been suggested but I wonder how practical this is for your setting. I would put a balloon on the recovery station and have the client use it like a punching ball for boxers.
Obviously, this is a compromise but if the goal is to keep the heart rate elevated during the weight training segments, this may help.