Probably not
The purpose of a co-signer is to add security to an otherwise unsecured and a risky credit deal, so if your parents’ credit is bad – they are no good as co-signers.
Is both of your parents’ credit bad? You only need ONE co-signer.
It also depends what exactly is bad on their credit report. I’d try anyway, and is the bank says that it’s nor good enough then you should instead take a secured credit card, and after 6 or 12 months of timely payment have it converted to a normal credit card.
Another thing is your job. The fact that you work only part time isn’t helping either. Maybe after you get a permanent job the bank will drop the co-signer requirement.
Good luck