Hi Jose - thanks for posting your question here.
Good first step: suggest your students see their doctor! Tendinitis can be tricky! As for how Yin might help the tendons, let's first talk about what Yin Yoga normally targets.
While we do target the connective tissues in Yin Yoga, we do not specifically want to target the tendons. In YinSights, I describe the way tendons work in a bit of detail (see
http://www.yinyoga.com/ys1_2.2.4.2_tend ... aments.php). Tendons are made up of the same material as ligaments, and they could be made thicker and stronger through yin exercises, but it is difficult to just target the tendon without also working the muscle. Since the muscle is more elastic, it will take most of the stress. The danger is, we really do not want to lengthen the tendons, as we do with the ligaments, as that would throw off our proprioceptive sense of where we are in space.
As you probably already know, tendinitis is an injury to the tendon or its sheath, which it slides within. The tendon may be slightly torn, abrased or inflamed. This can be caused by overuse (over exercising), repetitive use, or disease. The treatments can vary as well.
In my own experience, the best treatment for tendinitis is to rest the area first. No point exercising tissues that are damaged, as that will just interrupt the healing that is occurring. Continuing to work the area when it is already damaged could make the situation far worse. I used to get this a lot when I played a lot of golf and tennis (tendinitis in my shoulder and elbow). Only when I stopped playing did the condition heal: until then I just kept taking anti-inflammatories, which are not good to take long term.
So, I would not suggest he try any "exercises" to help with his tendinitis, however he may lessen the chances of it re-occuring by strengthening the muscles around that spot, so there is less stress on the tendons in the future.
In short: see the doctor, let the area heal before doing more exercise there, once it has healed do some muscular (yang) work to lessen future strain.
Finally, you didn't describe how the conditions arose, but improper Yoga alignment can affect the tendons. Make sure you students works with a Yoga teacher who can look at his postures and ensure that he isn't harming himself through his Yoga practice.
Cheers
Bernie
ps - here is an article by John Friend talking about tendinitis you may find a bit helpful...
http://www.yogajournal.com/for_teachers/513