Good ideas already, but I'll throw a different thought out here.
Think of this - if you can take a big practice swing without hitting a ball and that swing is as fast as you need it to be when you're on the courts, mission accomplished. What you need to also focus on is better movement and earlier preparation. That will set you up to start your bigger swing early enough to hit the ball on time.
Lots of players who want to hit harder assume that they only need to swing faster, but it's often an issue of swinging earlier. Some cars take longer than others to accelerate to 60 mph, but most all of them can do it, right?
Lifting is a good idea for helping to swing faster, but developing that strength is also especially good for holding your body parts together. Anyone can swing hard once, but lifting and getting a bit more muscle together will also help you to swing hard over and over without breaking down.