In the first paper below, they studied how much it takes for a healthy tendon to grow by adapting to stiffness when exercising. It is suggested that tendons change slowly after more than 8 weeks of exercises as long as the loading being put on the tendons exceed 70% of what they can withstand (e.g. 70% of the participant's weight for Achilles tendon).

The second paper states that the 12-week eccentric exercise program (3 sets x 15 repetitions twice a day, more than 6 days a week) was effective in treating the Achilles tendon problem. Therefore, it can be concluded that it takes about eight weeks to change a healthy tendon, and about 12 weeks to change a painful tendon.

However, the exact duration may vary depending on the individual and the affected area. If your pain does not allow you to exercise the affected/weak tendons with more than 70% of the load, it may take longer. On the other hand, if you effectually reduce the stress on the tendon through an effective exercise program, the pain can disappear within a 4-8 week timeframe. You will have the best chance at shortening the recovery time with this program.

References

Bohm, S., Mersmann, F., & Arampatzis, A. (2015). Human tendon adaptation in response to mechanical loading: a systematic review and meta-analysis of exercise intervention studies on healthy adults. Sports medicine-open, 1(1), 7.

Beyer, R., Kongsgaard, M., Hougs Kjær, B., Øhlenschlæger, T., Kjær, M., & Magnusson, S. P. (2015). Heavy slow resistance versus eccentric training as treatment for Achilles tendinopathy: a randomized controlled trial. The American journal of sports medicine, 43(7), 1704-1711.