Amex Green Amex Gold Delta Rewards Discover IT ABCO Rewards Visa + a few subprimers! 
It's easier to get approved for one of their charge cards and as opposed to a revolver. The Zync used to be the easiest to get, but since they've discontinued it the consensus seems to be that the Green is their entry level card. Since your scores are in the mid-600s, that would probably be the best Amex card to attempt.
Starting Scores for 2013: EQ 723, TU 735, EX Credit Sesame 751
Current Scores: EQ 733, TU 724 (05/01/2013), EX Credit Sesame 725 (05/08/2013)
Goal Score: 740+ FICO scores
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Cards: Cap1 Venture 6.4k, Cap1 NHCR MC 750, BankAmericard 1-2-3 Visa Signature - UCF Alumni Association 5k, Discover 4k, Citi Diamond Preferred MC 7.55k, Wells Fargo Rewards Visa 7k, Chase Freedom 5k, Chase Ink 7.5k, Amex Green NPSL, Dillard's Amex 7.5k, JC Penney 4.2k, Kay Jeweler's 5.1k
NY- I would say based on what I have seen and heard and read, that an Amex Charge card (Green to Platinum) are the easiest to qualify for, with the Zync being the easiest card for Amex to get approved for. Now, the Green I would think is entry level to get approved for. I am personally going to try for the Green or the Gold. The easiest revolvers from what I have seen to get approved for are the Delta Gold and the Hilton card. The harder ones to get approved for are the SPG and the BCE or BCP. Like tinuviel said in the previous post, it would be better for you to try for the Green because of you scores. If they had the Zync or they bring it back, you could qualify for that as well.
Well, I don't think the Zync is upgradeable. But from what I have read, if you have the Green card, and you have some hisotry built upon it (i.e. you have had the card for 6-12 months) and everything looks good, you can ask them to upgrade for you to the Gold, because I have heard they use the same underwriting criteria for all of their charge cards. However, it is another inquiry if you do get approved for the Green, because the Zync for some reason is/was not allowed to be upgraded.
What does your credit profile look like? You may be in the running for an Amex Green if your file is decent.
Do you have other credit cards with history? What is your income? Do you have any negative accounts or remarks?
All info will help us to know whether you would be in line for an Amex charge card approval.
Starting Score: 08/29/2011 TU 671 EQ 674Current Score (myFico + Amex): April 2013 TU 754 EQ 694 EX 694
Wallet: NFCU Visa Sig 25k, Amex Lowes 22k, NavCheck 15k, Amex PRG, Amex Zync, Discover It 13.5k, Amazon Visa 5k
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