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Is there any provision in the CGA for vehicles bought privately? Some details of the vehicles history were not revealed until after the sale. The seller has credited me $500 in acknowledgement of the problems we are having but the repairs have totalled around $3000. What options do I have?

No, the CGA doesn't apply to a private sale, but Fair Trading Act etc does apply. Therefore, if the vehicle was misrepresented in some way (eg; seller claimed it had done 20,000km but it had done 40,000 or made some other false statement about the vehicle), then you have some recourse.
However, if the seller made no representations, it's really up to the buyer to do their own due dilligence, and part of this can be to ask the seller specific questions, to which the seller must not provide false or misleading answers.

Thanks for your comments. I guess if you wanted to claim under the FTA it would probably end up in the small claims tribunal.

Correct. If you believe the seller misrepresented the vehicle, you can have the matter heard by the Disputes Tribunal.