Well technically speaking, there are no such thing as American Express "bad credit" cards. As you know, AmEx is known for being extremely picky when issuing credit. But although there isn't an American Express for bad credit, a number of forum members have reported success in getting approved for their new Zync card.
There are posts from 18 and 19 year olds, those with credit blemishes, etc. that reportedly are getting approved recently for this card. However on the flip side, some some have actually reported getting denied for Zync but ironically being able to get approved for the Gold charge card and Delta SkyMiles Gold instead. To find out more, check out the American Express Zync review