Reducing topspin if you're not meeting the ball near the centerline: If keeping your head still doesn't get the ball onto your racquet's centerline often enough to satisfy your arm, try hitting less topspin. A flatter swing makes hitting your centerline easier, as you're swinging more into the ball's path instead of cutting across it. Without the benefit of topspin, you won't be able to hit as hard at a given height, but slowing your swing down and hitting less hard will also benefit your arm.
Slowing your swing: Even if you can hit your centerline pretty consistently with a topspin stroke, a slower swing will benefit your arm. The forces that hurt your arm are proportional to the force of the collision between ball and racquet, which is in turn proportional to the opposing velocities of the racquet and ball. You have control over the velocity of your racquet. You can't completely control the velocity of the incoming ball--unless you choose opponents who don't hit as hard--but you can keep a hard hitter from using his full power by a variety of tactics, such as sending him balls that are above or below his wheelhouse.
Using the physically (vs. mentally) optimal grip: Make sure to use the grip that's most comfortable for each of your strokes. A Continental grip, for example, is painfully unsuitable to hitting forehand topspin groundstrokes, as is a full Western grip for hitting backspins (slices). At the net, a Continental grip makes much more sense, because it allows you to hit forehand and backhand volleys without switching grips, but on the forehand volley, it can be quite uncomfortable for some players. If you can get used to Continental volleys, you'll be able to react faster at the net without thinking about your grip, but for some players, switching between the Eastern forehand and Eastern backhand grips is so much more comfortable physically, it's worth the added mental challenge of having to switch.
Playing lefty: If you love being out on the tennis court more than your right arm does, give your right arm a rest by playing lefty. At first, you'll probably find some strokes, especially serves, quite awkward, but you might eventually become competent enough to give a decent match to a friend you would play righty, but beat fairly easily. Your friend will probably enjoy finally taking a set off you, and because you won't be able to put shots away as you would righty, you'll end up running like crazy and getting a lot more exercise. Playing lefty is also a great solution if you want to rally with someone who would be completely frustrated trying to handle your righty pace and spin. Trying to hit softer balls righty to accommodate a weaker player can strain your right arm while you're getting used to it, because you have to learn to restrain high-powered kinetic chains that have become natural from being used thousands of times. The feeling of those kinetic chains doesn't automatically transfer to your lefty swings, so you'll naturally hit an easier ball, and you and a weaker opponent will have more fun.
Sources:
Babette Pluim, M.D., Ph.D. and Marc Safran, M.D. From Breakpoint to Advantage: A Practical Guide to Optimal Tennis Health and Performance. Racquet Tech Publishing, 2004.
Howard Brody, Rod Cross, and Lindsey Crawford. The Physics and Technology of Tennis. Racquet Tech Publishing, 2002.
