I.have a green card and would like to apply for a Chinese visa.

Carine, you should find a Chinese partner who can send you the invitation letter. He/she should be able to help you acquire the invitation letter issued by duly authorized unit too. Then you can bring these two invitation letters together with your passport, filled application form, a recent passport photo, financial proofs (bank statement) and accommodation and return air ticket booking (if required) to the Chinese embassy in Georgia. Forget to say, your valid resident permit in Georgia is also required.

Mail application is not accepted anymore. You have to submit on your own or assign your friends and families to submit on your behalf. Or you can find an agent to help you.