It sounds like she has no credit history, and that's why she's being denied.
Being an AU on your card would definitely help. It would take six months from the month that she went on for it to generate a FICO score for her, although it's possible that she could get a card on her own sooner.
If you want to do this, I would advise doing it in a very businesslike manner. Don't get a physical card for her, and ask her to agree not to use the account number to shop on line. That's terribly unromantic, I know, but IMO it's a bad idea for two people to mix credit, no matter how tight they might be. In addition, I'd say that she should get with a local credit union, open up a share account (credit-union-ese for savings account), set up a direct deposit of $25/ paycheck or something, and in 3 months go talk to them about getting a card in her own name. It might well be a secured card, but there's nothing wrong with that; that's how you get started.
Once she's able to get two cards in her own name, she should be off and running, and you can drop the AU status.
* Credit is a wonderful servant, but a terrible master. * Who's the boss --you or your credit?
FICO's: EQ 781 - TU 793 - EX 779 (from PSECU) - Done credit hunting; having fun with credit gardening. - EQ 590 on 5/14/2007