Ok, she got the Citi DC so that's a great start. If you don't have a problem with Cap One, they've got the Quicksilver Visa Sig and Venture Visa Sig, which are some really awesome cards (I believe the minimum SL on these sig cards is $5K, so that would be a good option). She can try Cap One's prequalify site, and see if she's got any offers. A solid offer will say that she's "Preapproved", and it will let her see the terms/apr that is in the offer. Cap One now has a new policy where you can only app for one card within a six-month period, so heads up on that one.
Since she was turned down by Chase and Discover (I'm familiar with these banks), I guess I would maybe recommend Amex (as long as she has a clean file). She's got the income to support an app with them (and can also include your income if over the age of 21), so that would be an excellent bank to get in with.
Two cards in her name as the Primary Cardholder would be ideal. DW needs to use her Citi card (btw excellent SL and APR), and, until she has additional card/cards, report a zero balance on her statements each month. This new card will definitely start her on her way! Good luck! 
I am guessing that all of your wife's history is being an AU. This means that as an individual her credit does not exist. Whenever she charges something it is your responsability to pay for it since your the Primary Cardholder. Banks are getting smart to the AU trick and can clearly see which accounts are primary and which are AU. Chase likes to do funky underwriting and is rather strict. Discover likes to see history but not too much since they dont like competition. Citi as you might have noticed likes to take calculated risks and thats why they jumped at the opertunity with a nice 5600 CL. Most of theirs are 1000-4000 on the first issue. A good idea would be to go ahead and have your wife get her own cards and loans. If you look at the credit score you will notice it is slightly lower since it is populated by AU and not actual accounts. If a bank pulls it then most AU status accounts will flat out be removed resulting in a blank report and a confused representative. My recomendation is to have a more equal distrabution of cards either by having your wife apply for the same cards that she already has or to stagar the cards so some are with her primary and some to be primary with you. That way you can be AU on her cards. Basicly now she just needs new primary accounts that she can show that she is responsable on.
If you average the credit score in the range you provided it would be 790. Its fine to do an App Spree and I recommend a minimum of 750 for that. Your AU for her is holding her score up for now but have her select a few cards to apply for. If you select right you can get 2 more ish. Try to do all the applications on the same day in the order you want them. Research the bank that issues the cards to find out their requirenments and what credit report they will be reading. You can literally plan the applications to get the best results by having diffrent reports be used for diffrent cards. Look for banks that are easy to get started in like BoA, Capital One or banks that use calculated risk like Citi as well as CU's which are consumer friendly. You can even try isolated lenders like Blispay. I can imagine a Regional Bank might want to play with her purely by credit score. Once the cards are open they need to grow in age and showing good payments. This will become her history and after 2.5-6 years it will be solid enough to withstand shocks.
P.S. The AU issue is because you can add anyone as an AU including people you don't know and never met. Some geniuses actually do that for money to have positive accounts report and the banks got smarter to stop that from happening. Its nothing personal.
@echoecho wrote:
Great thread with AU issue but how does CCC treat co owners on a cc. CUs allow co owners on a cc, is it treated as AU or individual. Thanks.
Co-owner is a CU specific term used by some CU's to discribe the two people who share a joint account. Each person should be a member of the CU independently and is a co-owner of the joint account. These accounts report as Primary for both people's reports. There is usually a limit of 2 people on a Joint account. There is no limit on AU's except what the bank or CU allows. CU's like to use diffrent terms for the bank terms of Individual Primary, Joint Primary, and Authorized User. Commonly the terms are Member, Co-Owner, and Authorized User.
THis is a situation i would have probably taken the Joint offer that sometimes discover offers for an account....even still i would have applied for another card as well..
(Even though she has a good score, its not a strong file... id wait a little bit.. UNLESS your applying for a card that can be a JOINT app.. not a AU)
Seems that few banks offer Joint accounts these days... But Credit Unions still do.....
Congrats on the DC .. ....
Might still want to go for another card or 2 later down the road (non joint) even if it has a reoccuring sub that autopays from a joint checking account....
I setup something like this for my mother... but she did have the advantage of keeping one card in her name and it didnt fall off... so BOA gave her quite the offer
and its basically only pulled out once a month or so to make a few purchases...
Not a goal to up score, but in this case,, up the quantity of trade lines in HER name...
Maybe even a Secured Share Loan might work .. (In HER name only).... Your thickening the file, which may fluxuate her score, but in the end it will probably increase
-J
I'm not a fan of pulling the bandaid off by cutting off the AUs all at once... Some issuers still take into account AU's at the same address.. but not as meaningful as it once was......
Others may argue .... but my thought is to shore up her credit thickness, than perhaps take off a few aus (not all) ... rinse and repeat, perhaps every year..... Id still keep her as an AU on a few cards... because its gonna take time ....
Were building credit vs rebuilding..... know it might seem late but if something happens... ideally id want at least 3 cards (eventually) in her name.. perhaps with you as the AU... but as Zero said.. your going to have to build it up...