The AmEx Zync charge card was hard for me to get; I apped for it two times before I finally got it! I read that the general criteria for the No Pre-set Spending limit card is: at least a year of credit history, 650+ FICO score, no major derogs on credit report. I hear some people who are on the border of acceptance criteria get counter-offered a Zync card that has a hard limit of $200 or $500 with auto-pay enrollment.
I applied for the student version of the Citi Forward card and I got it once I had about 4 months of credit history. They did verify my identity, school enrollment status, and financial information though, so they are strict on that. Once I sent everything in, they gave me my highest credit limit so far.
On another note, my Experian FICO score is 707, according to the letter I received when I got my Bank of America Cash Rewards card last week. Not too shabby!