Is there anything keeping her from getting a secured card? Toss $500 or $1k into it for a year, use it, cancel it, and get your money back.
Or there was that OSU Credit Union near you that offers a Visa Value starter card.
As far as Citi, Amex, Chase go specifically... Some people claim the Citi Aadvantage
is an easy card to get, but it has a $95/year fee, waived the first year. Some people recommend the Delta Gold Amex
as an easy card to get, but it has a $95/year fee, waived the first year. Some people recommend the Chase Amazon card as an easy-to-get card, but there's a review on this site
that isn't so enamored of it.