Take what works and tweak it slightly
Earth already has vast mountanous areas such as the Andes, the Alps, and the Himalayas, without being an unlivable hellscape of earthquakes and volcanism. So make your planet very Earth-like with just three adjustments.
Mountains sink into the ground very slowly over the course of millions of years due to gravity. It also determines their maximum height. If it's lower, then they would sink slower and be taller. You can change the gravity very slightly, so that your world remains as Earth-like as possible.
The atmosphere of a planet erodes its mountains, so having a thinner one means erosion would be slower. Again, you can change it slightly, so that your world is Earth-like.
More continental fragments
You can have your continent be made up of several smaller plates, rather than a single big one. Similar to how the Indian continental plate pushes north into the Asiatic plate, creating the Himalayan mountains and the Tibetan plateau.