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My wife was in the same situation last year in September. Only AU on my Citi and Amex, nothing else. 0% util, 0 INQ and an EQ FICO of 784. She applied for the Citi Platinum Select and got approved for a CL of $2000. However i have to admit, that we are banking at Citi. So maybe it is worth a try, before you start with Cap1.
LEXiiON
You can always go to Discover and see if you preapprove before hard hit.
concorduser posted a few threads in the past week on getting cards for their daughter who only had AU's on her account - they might be helpful to OP.
If I recall, it worked out nicely.