Have them add you to two older non-Amex cards that have a high limit and report a low balance.

Give it about 30-45 days to show up on your credit report.

In the meantime I recommend you go on www.annualcreditreport.com and pull all 3 reports. They'll probably ask you to mail in with 3 forms of ID. That's fine, do it. It'll help in the next step so when you apply for Discover card they can verify your name, SSN, etc with Equifax, etc.

Then I recommend you start with unsecured Discover card.