Every time she brings stuff up, suggest a therapist.

"That sounds rough, have you thought of talking to a therapist?"

"It sounds like you're dealing with a lot. Did you look into a therapist yet? They can be really helpful."

"Geez... this seems beyond me, you'd be better off with a professional."

Friend: I don't want to get a therapist, I just need a friend to listen.

"You have a lot to talk about, and it's beyond what you should expect from a friendship, not that I don't want to help. The occasional shoulder to cry on is one thing, but you have stuff you need to address, and that's just above my paygrade. It's not healthy for you or our relationship, either. Want me to help you find one?"