There's a response I heard discussed re working with teenagers and I think it was excellent! This is how I remember it.
"If you really feel suicidal you need proffessional help and there's no way I can offer you that. If I begin to try the chances of me getting it wrong are too high - it's out of my depth. If you tell me now that you're going to do it I will have to contact (insert appropriate emergancy service) but that is the best I can do. You matter a great deal and no-one wants to lose you but (in the Uk) the Samaritans are better qualified than me to help, their number is (insert US suicide line number)."
Obviously with children it's a case of then declaring child protection means you can't keep confidence of the conversation. However if it was an adult friend I would also add that I would not keep confidence (keep secret) suicide threats if I felt it put their life at risk to do so.
The rest like above, a broken record because I KNOW I am NOT qualified to give the best help and won't replace it with what could be disasterous second best.
Hope that helps a little. My Mum used to threaten to be having a heart attack when disagreed with. In the end I got wise to it and would ask if she would like an ambulance, when she refused I would say it was her responsibility but if she actually passed out I'd call one anyway. It's one reason I won't deal with suicide stuff myself except for the above - I've got personal issues about the 'threat' of someone saying they will die and I think those issues make me really BAD at being understanding - it doesn't mean I don't care though, just that I won't take it on at any price.