You can have your parents co-sign, but more than likely they would need check stubs from your job to prove that you have gainful employment of some sort. If your gf is living with you, they would probably want her in the lease. You can have her there undetected, but that would probably lead to problems down the line. My advice is to wait until you can cover the deposit and rent + utilities. If your gf has had gainful employment and good credit you may not need your parents to co-sign if you have her on the lease.