Thanks to everyone who replied.
Most replies say pretty much the same thing.... eat peanut butter and icecream, and if that doesn't work, nothing will. But she already has been eating that stuff and it hasn't worked.
So, I'm helping her through some exercises we can just do at home. She doesn't want to go to the gym, so I've come up with a few basic movements we can do using our own bodyweight, and two plastic bags full of pennies.
As for those who don't understand her wanting to gain fat.... I guess none of you have been skinny. In my opinion, she's not skinny.... she looks perfectly normal to me, just slim and slender. But my opinion doesn't count when we're talking about her self-esteem. She thinks she's skinny and she hates it. She just wants her arms and legs to be a bit thicker etc.... and while she doesn't want to be obese or even overweight, she just wants to gain a little more padding. Just like fat people want to lose fat because they think it's unattractive, she wants to gain some because she thinks being skinny is unattractive.
Having said that, what are some good exercises you can do at home without any equipment? I've got her doing pushups, dips, squats, lunges, leg extensions and leg curls (with an ankle weight), calf raises, dumbbell presses (with our makeshift dumbbells), lateral raises and some biceps exercises with the dumbbell money-bags. Obvsiously we don't do all of these at once, but break it up over two or three days. I can't seem to find a good exercise for back. I think next time I'll get her to do flyes as well.
Hopefully this will give her appetite a bit of a boost, and she can gain some muscle and/or fat.
Thanks.