The standard conservative protocol for tendonosis is eccentric exercises. But if you've delved deep into the subject you've probably come across other protocols, most notably "heavy slow resistance training". There are starting to be some studies comparing the two and it appears they are roughly equal, but patients prefer the heavy slow resistance training protocol:
http://ajs.sagepub.com/content/early/2015/05/27/0363546515584760.abstract
But I think there is an even deeper lesson. Both protocols will train tendonosis. There is nothing special about eccentrics. Concentrics work too. So really what you need is to make progressive increases in load while staying within the adaptive zone. Too little stress (like completely stopping all activities and resting) and you won't provide enough stimulus to make your tendon stronger. Too much and it will break down more than it can heal.
I read a thread on a cycling forum about patellar tendonitis and someone said that they just cut back on the hills until it feels better. I suspect cycling could also make a good protocol for tendonosis. In fact, it might be ideal because unless you are doing intervals uphill, it would be hard to overdo it on a bike.