Try First Pornabanc NA
There ain't no such thing really. In fact, I was told you can charter a private bank in Luxembourg with just 9 million Euros capitalization.
Look for a bank that is real shaky. Publicly traded bank who's common stock has perilously fallen ... they won't ask too many questions.
It's about reputation management on the banks' part. You are not that important even if you have over $1 million on deposit -- except to a bank the needs the capital badly ;)