Sorry to hear about your denial. What reasons did they give you for the denial?
Unfortunately, as far as I know, this site is primarily for US customers, so I do not know if you will find your answers here.
Here in the US, the Amex charge cards (Green, Gold, Platinum) are easier to obtain than a "revolver" (i.e. a credit card like Blue or Australia's Qantas AMEX).
I would recommend looking at the reasons for your denied application for the Green card and see if anything has changed in your credit profile. If they denied you due to income, than you know that you will need to wait until you earn more. If they denied you for a late payment or having high balances than I would see if the late payment creditor will "goodwill" the late payment off. If you have high balances, you will need to pay those down before applying again.
Without knowing your specific reasons for denial or even what Australian credit standards are like, I cannot really give much advice.