what would be a good co-op game?

You could always do some bro-op in Broforce.

Get her to try FFIV, V, and VI. Also Lunar, Xenogears, and Suikoden. They aren't co-op, but she can sure give them a go when you aren't around to co-op with!

Trine is great

Worms Reloaded

It has already been mentioned, but only briefly. Try Neverwinter Nights (the original game). You can buy it from GOG and probably run it, and there is no end to the modules you can download and play. (You said she likes stories. Each module is a different story.) Just make sure the module you are playing is for 2 or more people.

Few recommendations:

Valley Without Wind 1 (not sure if she would like it since it's also about crafting etc, check Yourself)
Valley Without Wind 2 (not sure if she would like it since it's also about crafting etc, check Yourself)
Heroes of Might and Magic 3 (there is a HD version on Steam)
Two Worlds 1
Two Worlds 2
Worms Armageddon (come on, who doesn't like those cute worms?:D )
Guacamelee!
Etherlords 1 (not sure if it had multiplayer though)
Etherlords 2 (not sure if it had multiplayer though)

Also, it's not on Steam (I wished it was though!) but I can recommend all of people here (Especially fans of SNES games) a game about Mario... Super Mario Bros X. I have never had so much fun playing this game with my sister (2 players playing at the same time) :) We have played it few months ago, now we started playing it again. It's awesome, especially when You remember SNES era (we do). Memories... You know, it's always good to come back to childhood times :D I'm sure everyone will love it!

PS> I know none of these are JRPGs or even similar but Icouldn't think of anything better.