Short answer to the above question: NONE. There is NO role for China in a "two-state solution".
Because….
The two-state solution is DEAD.
The sooner the world comes to terms with this, the sooner we might get to some sort of peace in the Middle East.
A peace that requires the removal of Hamas. Because Hamas have only one aim: the complete genocide of every Jew in the world. That is no partner for any kind of "two-state solution". They don't want it and never did.
We must not forget: the two-state solution has been on the table since the 1937 Peel Commission and has been re-offered no less than eight times. Each time, it was the Palestinians that rejected it.
Pushing for a "two-state solution" is a kind of a weird mantra: that people like China's leadership, feel better repeating. A kind of Buddhist Chant. Nan Wu Ah Mi Tuo Fo. Ohhhmmm….
But:
It's. Not. Viable.
There. Is. No. Two-State. Solution.
Period.
PS: Famous international affairs "realist" professor John Mearsheimer has been a "long-time advocate" of the two-state solution He now says it is not viable. It's done. We have to move on.