One way of doing it is traveling to Greece. Only have tickets to Greece as your final stop. We normally do this anyway. Travel on Australian Documents.
Then when in Greece, get return tickets to Cyprus. Travel on Cypriot Documents so that the Cypriot stamp isn't seen on your other passport.
However, they get you to fill out a declaration before the plane even lands in Australia which are collected by customs. They ask you what countries you have traveled to. You will have to not divulge Cyprus. Now that is a lot easier said than done because if they catch you lieing, and no one really knows how they collect information, then you are stuffed.
So don't just contact the Cypiot Consulate. You will also need to contact the British Foreign Office to see what they have in place, because is a double edged sword.
potentially, you will be fined and/or charged for falsifying Federal Government documents and that's a very serious charge. Also, you get placed on a watch list. And it could have repercussions when travelling to certain countries like the US and Canada. Yes they share information.
It is far more easier not travelling to Cyprus and sleeping easy at night.
This is what these restrictions have done. It has made it dead easy for jurisdictions like Australia to control the travel habits of Australian Citizens. If they don't want Australians to travel to Cyprus, they now just use the Chy-na Virus excuse to restrict travel to Cyprus.
Onya's all you cupcakes and do gooders.