What reason did they give in the written explanation for denying you credit (which they are required to provide if asked)?

Given the credit cards you already have and your income, I agree that your chances are probably slim (and Citi is probably wise, at least statistically if not in your particular case, to deny you credit here). However, it's well worth knowing the specific reason.

My first application for the AAdvantage card was denied because of insufficient credit history. When I had Citi send me the credit report they relied upon to make that determination, it was missing a mortgage which I had paid off about a year before the application. When I sent them documentation of the missing piece of credit history, the application was approved immediately. Make sure that they aren't missing information related to the reason they denied you credit. However, length of good credit history is an important factor, and there's nothing you can do except what you're already doing and time to build that up.

I doubt that income that is not yours will count if you're applying for credit in your own name. I also don't think a card on which you are not the primary account holder counts for or against you because the credit is not in your name.