Before wasting inquiries, get your scores up a bit. If you can get TU over 600, these are several cards that will give you a YES (store wise) which can convert to a co-branded (eventually), i.e. Macy's, Wal-Mart, Target. In my experience, GEMB products have been easy.
Do you have Crown Jewelers? Sterling Cards are also fairly easy (Jared, Kay, JB Robinson). If you get one, you'll usually get all three.
Just be careful with your app's.