Tennis elbow is usually caused by the tearing of tendons during eccentric contraction of muscles around the elbow. Last year, I got tennis elbow from using a kettle bell that was too heavy for me. The solution involves lengthening and strengthening the tendon.
The Thera-band The Theraband Flexbar is a grippy rubber bar which allows you to do the exact exercise you need to help this problem. I became very depressed reading about how some people never recover from tennis elbow, but after 1 day of using this tool, I started to feel relief. Complete recovery took about 2 months for me. I first read about it in the New York Times. I urge you to try this.
Make sure you know if you have tennis elbow or golf elbow first. These are injuries to different parts of your arm.
There are also two stretches that can help.
Hold out your injured arm straight, with the palm facing down. With your other hand, pull your fingers down so your palm faces you.
Hold out your injured arm with your palm up. With your other hand, pull your fingers down and towards your body so that the palm faces away from you.
These stretches felt good to me, and helped, but the exercise was the most important part.
Good luck, and please report back on success or failure.