US citizen needs to renew Chinese visa in Sydney

I think you can give a try but I don't know if you will succeed. Perhaps, you should confirm with the CVASC branch in Sydney if you can apply there. Thanks to the new visa rules, the applicants who apply in the third country or region are required to provide their resident permits for employment or study or other legal status proof.
Contact information of CVASC branch in Sydney:
Call:+61-2-94758800
Fax:+61-2-92612088
E-mail:sydcentervisaforchina.org