I looked into this a while back because I wanted to put some portion of any trip on my Citi Prestige credit card, which has excellent trip delay coverage. After spending a lot of time researching, I found one online travel agent that allows payment with two cards: CheapOAir.com. As far as I can tell they are the only option.
I think is possible toit's also usually possible pay with two cards in person at an airline ticket office like an airport ticket counter, but sometimes there are also locations in big cities. But I don't know if that's true for every airline (or even true at all).
I decided not to use CheapOAir, because there are many complaints about their customer service, and if I remember correctly, a tendency for them to sometimes inexplicably cancel reservations. I'd suggest you do your own homework about them and make your own decision.
Also, just to see if they still allowed payment with two cards, I just did a dummy flight booking search on their site (one way NYC>MCI 7/17/18) and it missed about half of what all the other search engines showed, and what it did turn up was more expensive than elsewhere. I don't know if it's an anomaly or a consistent issue.
If you really wanna get stupid about this, you could fly Southwest, which lets you cancel flights without penalty. You could book a cheaper flight to some arbitrary place with your card, cancel it, and the value of the ticket would go into your Southwest travel bank. You could then apply the travel bank funds to the booking you really want and put the balance on her card. For other airlines, you could try experimenting with their 24-hour refund policies, or their fully flexible tickets -- if you can get them to issue you a travel certificate rather than a refund to your credit card, you might be able to accomplish the same thing.