I don't think it's that easy to tell, especially not on the internet. A better question might be, how do you reach out to people suffering in silence and convince them it is okay to talk? (An anonymous online suicide hotline which doesn't report cases to the authorities might help, but I suspect it would be trolled.)
I just heard this on NPR this morning, so I may not have the specifics: Apparently, FB will provide a link that somebody can click if one of their friends writes something that friend thinks indicates their friend may be having suicidal thoughts, and their friend will get a message for a real-time chat with someone from a suicide prevention place.
And your point about it not being easy to tell is very true. This is why the thought about the virtual chaplain. People would hopefully carry enough real-world positive thoughts about chaplains into their virtual dealings to feel comfortable "talking" with an online chaplain. If a community had a designated chaplain, that person would be known to the other members of the community and anyone with issues would be encouraged to have confidential communication with that person. (Chaplains being licensed religious ministers are usually permitted by the law to keep the contents of conversations private ... except in a few very specific cases such as child abuse mandatory reporting situations.)