You can transfere your CAAC licence, but if your not type rated with time on type it might be difficult to get a job. It can also be difficult to transfere your licence because you need to Chinese labour buro to confirm that you no longer fly for your old company and that your contract is cancelled (the so called realease letter from your current company). Its not the Chinese CAAC who do this like most people seem to think.
For 737NG jobs there are a few companies. Shanghai Airlines, Hainan (beijing based) and Okay airways. I'd recommend them in that order but i'd strongly recommend staying away from Okay. Also i've heared Xiamen might start recruiting in the future.
Also there are a few foreign FO's flying in China, if you can get introduced by someone its possible. If you dont have some relationship its practically impossible.