A Registrar can refuse to sign a private CAN.
Most likely, the Registrar thinks that
regulation 8.4 of the Local Court Rules 2009 applies to your proposed case.
‘A registrar must not sign a court attendance notice, or an application notice, in proceedings commenced by a person other than a police officer or a public officer if of the opinion that the proceedings are frivolous, vexatious, without substance or have no reasonable prospect of success.’
You can make an application for a Magistrate to consider whether or not the Notice should indeed be signed.
If that Magistrate say no, then that's it, you're finished.
One other thing - before you start, make sure that you have enough money on hand
to pay both your costs and theirs when you get your prosecution fails, or simply gets dismissed.