Squats WILL make your knees stronger, as long as you do them correctly. You need to force your weight on your heels, and pretend you are pushing the opposing walls OUT with your KNEES (ie. push your knees out!). Bend at your hips, ass OUT, back STRAIGHT.
Before I improved my form, my left knee hurt like a b!tch after doing squats. Going up/down stairs was killer. Now I've improved and it's made such a huge difference.