China has had several 'conquest' dynasties, whose origins were foreign invasion. There were the Liao, the Jin, the Yuan and the Qing. All of these dynasties attacked and conquered China (or part of China) from the north. The challenge here is to have a scenario where a non-Han dynasties is built from a conquest coming from the south. A Tibetan dynasty getting established during the height of the Tibetan empire is probably the only one I can think of, but are there any other possibilities? Could one of the indigenous ethnic groups in southern China claim the Mandate of Heaven? Could a Thai or Vietnamese based dynasty work? The later the PoD is the better, and bonus points for lasting over a century.