Can the co-signer report the car stolen if primary is not making payments and messing up your credit rating?

If the car was not stolen then no. That would be a crime. You co-signed and now you are libel. Go to the bank and talk to them about it. Ask them the re-posses the car. get it and the dead beat out of your life.

You're kidding..I hope. What you propose would be filing a false police report. Which would get a lot of people in trouble. Especially you, and besides a hefty fine, the possibility of losing your driver's license (depending on your state laws). You might very well go to jail. Which IMO is worse than a bad credit rating.

Definitely Not.You might be guilty of fraud for making such a report.