I would recommend the following:
Upper body ergometer
Upper body resistance training doing it in a circuit fashion
I would also add balance training and core training for this individual. This will stimulate the neuromuscular system to help prevent injury and unwanted joint motion. It will also enhance neuromuscular efficiency for more intense exercises later on
The biggest thing is a workout needs to be one that they will enjoy and stick with ( even with limited mobility). Keep it challenging yet feasible for the client.
She could perform a lateral two step with her arms over her head. She can do an isolated twist her hips still and raising her arms overhead. She can perform toe taps forward/side and back and include corresponding arms. She tap her toe to each corner of the recovery board. She can do heel shuffles.
Hope this helps!
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.