I'll like to suggest this list for the ruling authorities of the Tibet catalough.
I couldn't really figure out when the split was, between the Guangxu emperor and the 13th Dalai Lama. As I understand it, it was more a gradual change from one to the other.
Tecnicly the Dalai Lamas just had to pay tribute to the Emprors before, but the Emperor is featured on some of the coins and where the defactor rulers of Tibet (and named after the emperors in the Numista catalough).
There may be some mistakes, but I tried my best with the sources belove and the information already provided on Numista. I'm not a historian nor expert in any way, but I hope it may be a help at least.
Tibet Autonomous Region of China:
Qing Dynasty
- Qianlong (1735-1796)
- Jiaqing (1796-1820)
- Gaungxu (1875-1908)
Dalai Lamas
- Thubten Gyatso (13th Dalai Lama) (1879-1933)
- Jamphel Yeshe Gyaltsen (5th Reting Rinpoche) (1934–1941) (Regent)
- Taktra Rinpoche (3rd Taktra Rinpoche) (1941–1950) (Regent)
- Tenzin Gyatso (14th Dalai Lama) (1950-1959)
Main source:
https://en.wikipedia.org/wiki/List_of_rulers_of_Tibet
https://en.wikipedia.org/wiki/3rd_Taktra_Rinpoche
https://en.wikipedia.org/wiki/List_of_Chinese_monarchs
https://www.britannica.com/place/Tibet/Tibet-14th-to-19th-century#ref71440
Video from Visual Politic, about Tibet:
https://www.youtube.com/watch?v=8qO_PJAzIIo&list=TLPQMTAwNTIwMjHXEtEggiyASg&index=23