Conjugal is not an option for you two (Canada-NZ) because there is nothing preventing you from marrying (or living-together 12-months continuous for common-law).
If you want to do common-law, she can apply to extend her stay here in a few ways. If her work visa is not extendable, she can apply to Change her Status, so possibly to go from a work visa to a visitor visa. She would not be able to work (she would have to show financial support from herself or from someone else, i.e. you). If she gets a visitor extension for 6 months, but you still don't have enough proof, she is free to apply for a 2nd visa extension.
She may also wish to look into applying for a study permit if she prefers, but that means going to an accredited program (can be diploma or certificate), etc. Poke around the CIC site and see what her options are.
The big, important thing for common-law relationship is the proof:
How can my common-law partner and I prove we have been together for 12 months?
There's a good list here; please note that it says at the bottom that "You do not need to include all these items to prove your relationship is real. Citizenship and Immigration Canada may consider other proof as well". So don't freak out and think that you need each item, but the more solid your proof, the more likely you'll get approved as common-law.
You need documentary evidence establishing 12 solid, continuous months of cohabitation. This is the big one. You can't have a gap or break of a month or two.
Also consult the region/country specific guide for her PR application, which will include things about having
at least two statutory declarations from individuals with personal knowledge of your relationship supporting your claim that the relationship is genuine and continuing
Statutory declaration means that it must be signed by the letter writer in front of a commissioner of oaths (or notarized, but the CoO is generally much cheaper).