Can't obtain penal clearance

[Kevinw]

Australian citizenship requires that you provide a penal clearance for countries that you've spent ≥90 days in while you had your permanent residence. I have been in China over several backpacking trips during this time, but will not be able to get a penal clearance because I never resided in one particular place.
What should I do with regards to my application documents? How can I prove on my application form that I am unable to obtain this for that reason?

 

[Adam1user]

The only way is to contact the proper authority in China and let them provide with some sort of any supporting documentation. But I am surprised why you can't do it, all you have to do it put a request, although you traveled, but I'm sure the authority has a database which can provide you with the clearance, the only thing that comes to mind, that it may take more time as they need to ask several places to check upon you.

 

[Tim W]

You need a 无犯罪记录证明.
In English, this is best translated as a "Certificate of Good Conduct"
(you'll see other, clumsier, translations)

As a foreigner, this document will probably be issued by the Public Security Bureau
(PRC nationals can also get it from a local Notary Public, but that's not relevant to you).

You will need to source this document from PRC.
It will take time (perhaps months) and cost money.
Have a look at this page, published by the Government of Canada.
You may find it helpful because the in-China process is pretty much the same for a foreigner of any origin.
Read it all.

The most efficient way to deal with this is to engage a law firm in PRC to assist you.
You may find this list helpful.
Perhaps you will recognise the names of two major Australian firms on the list.

Best of luck.