Got nada for this challenge. I have loved many a suicidal thinker over the years, yet nothing I’ve ever said - kind words, hopeful words, begging, pleading, joking, encouraging, trying - has ever made a damn bit of difference.
I gave up on those methods and have switched gears now. Rather than wasting words, I’ve instead learned to just be there. Physically, if possible, as it seems best.
Don’t let them alone, particularly on bad days. As suicide seems a private affair simply denying that privacy with constant companionship seems the best solution. Even - or especially if - they don't want it. There's a reason there are no doors in suicide watch.
Obviously professional help is the way to go, but even after seeing someone the road out of darkness is best not traveled alone.
It can be difficult to companion someone who really doesn't seem companionable, particularly when their mood can exhaust your own. Which is why it's much easier to form a party. Taking turns taking care of someone, and making sure they have multiple sources of comfort, can help immensely. Keeping everyone charged is equally important.
As the Net memes say, Winnie the Poo and friends make excellent caregivers for the perpetually dreary Eyore; they never force him to be happy, they just continue to invite and include him on their adventures regardless.
How long you keep this up depends on the person. Suicidal people have to find their own reason for living; you can't give them one, or be one for that matter. Took me many miserable ages to learn that one. You can only stand watch, and keep them moving along, until they find it on their own.
And if it all fails, then it's important not to internalize their loss as your failure. People make their own choices. Nobody said life was easy; that goes doubly for the ones left living. Focus on the ones not yet lost, and keep yourself moving too. I don't think there's any shame in that, even if it may sound cold at times.