What are some good exercises to relieve my pain from wrist tendonitis?

Wrist tendonitis? Is it acute? Or chronic? What did your doctor told you? Did you have an mri? Did you have an ncv/emg? I need more info in order to give you a good answer.
Rest. Depends on the kind of tendonitis. In general, it is best to rest the inflamed tendons by using a splint. If the tendonitis is on the thumb side of the wrist, it may be dequervain's tendonitis. In that case, a standard wrist splint will not be enough. You would need a wrist splint that has a thumb extension (thumb spic splint). Otherwise, a standard wrist support and very gentle stretching.