What are your FICOs? AMEX Delta Skymiles is supposed to be the easiest to get.
With FICOs in the mid 600s, with no AMEX default in your past, and you should be good for an AMEX Delta Skymiles. You can apply online for multiple AMEX cards, and if you do it all same day at most you'll get 1 INQ per CRA. Might try an AMEX Green and a Skymiles.
When did you default, when were you issued an AMEX card again, and what were your FICOs when you were issued a card the second time?
AMEX blacklisting is well confirmed by LOTS of people, here and elsewhere. I have probably talked to a few dozen who can attest to it.
If your FICOs were high enough, or your default was a long ways in the past, or if you got your AMEX the second time more than a couple of years ago, then yes you might have avoided blacklisting.
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Hmmm...not an outright denial. I have not heard from them, so I wonder if a human is going to approve it instead of a computer.