As a lifelong bodybuilder and construction worker, I suffered with tendonitis all over my body for most of my adult life--specifically in both of my elbows. I tried everything you could imagine--acupuncture, active-release technique, etc. Eventually however I found the cure to come from a combination of two supplements: bromelain and cissus.
Here is a quick explanation of the anatomy behind tendonitis. Think of your tendons as ropes or cables that operate to pull your muscles and joints like a machine. When these ropes or cables are put under strain, or are weakened for some reason, they tend to fray under the tension. When your tendons fray, tiny fibers poke out from them, just like a frayed old rope.
Now, all tendons are contained within a "tendon sheath, " and the tendon moves back and forth within that sheath as you move your various body parts. When a tendon is healthy and smooth, it moves back and forth within the sheath smoothly. When a tendon is frayed, however, it creates friction as it moves back and forth in the sheath. The inflammation that results from the tendon's frayed fibers constantly rubbing against the tendon sheath is--you guessed it--tendonitis. In theory, the body should eventually be able to digest up the frayed fibers and heal the tendon, but anyone who's had tendonitis knows that this process can easily take years.
Now here's why the remedy works: bromelain is a very potent protein-digesting enzyme derived from pineapple cores. When you ingest this enzyme, it basically enhances your body's ability to digest up any sort of scar tissue, etc. , built up in your body. The frayed tendon fibers causing your tendonitis are precisely the sort of dead fiber that bromelain helps to digest.
Although bromelain by itself works very well, I have found that adding cissus (an herb known for healing joints) together with the bromelain brought me back pretty much good as new. Just remember to take the bromelain on an empty stomach, otherwise it will simply digest whatever protein happens to be in your stomach and you will have wasted your money.
Finally, while topically-applied DMSO and drinking apple cider vinegar also have a good reputation for helping tendonitis and inflammation, I don't think they're necessary, although they are both excellent remedies and adding them certainly won't hurt you.