How does a client not feel like crap about tell their counselor....?

They are trained for this and it is part of their job. I think they would feel worse if you didn't tell them and something bad happened to you that they couldn't help you with. You are paying them lots of money and it is their job. Don't feel bad, don't feel bad at all. Every job has some hard aspects and this is the job they have chosen, so let them do their job.

Here's the thing. A client must never feel like they will be treated like crap at a psych's clinic. The psychologist must listen and attend to all of the clients concerns. Point blank, a client comes because they need guidance. If they do not feel comfortable they shold not go. Also dont make the client feel like crap talk to them and if they made a mistake talk to them as if most people make the same mistake in life.

If the client is on suicide watch or something, then the councilor should forget the privacy and get a councilor that specializes in suicide.

Well, if you are not a psychiatrist, you definitely need to refer them to a psychiatrist. Is there some kind of in-patient treatment center you could refer them to for an evaluation? Here in MN when a person makes threats like these and/or acts on them they get sent to this one hospital that does an evaluation and the doctor they see determines whether they need to be admitted or not. If you don't think they will go, don't give them all the details, tell them you would like them to get a second opinion at such and such clinic/center and YOU make the appointment for them.