depends on what you definition of private is I guess.
I fly a lance and got the job with 320tt. You can find private companies that fly anything from 182's, 206 & 210s, Lance's some piston twins (CSG in darwin run a few lances along with a Partanavia and a jet) right up to corporate jets.
Generally with these companies you'll be required to do more than just fly. I am a representative for the company as well as the pilot, therefore when I'm not flying I also deal with customers etc. Hours may not be as good as charter but the cash and conditions, plus not having to deal with the myriad of egos that exist when you first start out in GA more than make up for it.
These companies don't generally advertise on AFAP or in the paper etc but can rely alot on word of mouth, but if you ask around, do a few CASA register searches the information isn't hard to find