You should lay off playing until the knee stops hurting. Pain (as opposed to just some muscular discomfort) is the way our bodies let us know that active inflammation is occurring. If the pain persists you should get it checked out by an orthopod with a special interest in knees in athletes.
You definitely need to power your serve with an equal push off from both knees. Using one leg will surely lead to an overuse injury that will keep recurring over time.
The way to make the "knee" stronger is actually to make the leg muscles stronger to take the stress off the knee. Squats are the classic weight exercise to add real strength to the knees. The leg press machine approximates the leg component of the squat, but doesn't provide any real back strength or balance. Thus most weight lifters decry the leg press machine as vastly inferior to the leg press, but if you have a limited goal of strengthening your legs to improve your knees, the leg press will be far easier to do than mastering squatting technique. And there are no shortcuts to real strength gains. You have to start with weights close to your maximum, but let you do 5-8 reps, and keep increasing the weight as you gain strength.
To help gain medial and lateral leg strength (as well as improving your footwork) to protect the knee, try doing court drills that include the following: lateral skips along the baseling, grape-vine steps, and alley drill runs where you are making sharp cuts back and forth.
I hope this helps. Good luck!
