John, are you prepared to have your wife 5150'd? Cuz if she mentions suicide in front of the counselor (an MFT?), as a Mandated Reporter they're obliged to commit her. Based on your recent description of how the situation has deteriorated, that may be the best outcome at this point. She's become inured to your entreaties, so outside professional intervention might be what it takes.
If possible, prior to the couple's session, you might want to talk just yourself with the counselor about your wife's suicidal ideation. In any case, make it the immediate & primary focus of the session, expressing it as your deep concern for her safety -- essentially ambushing your wife, sorry, don't tell her in advance you wish to focus on that. (NB: remember to address everything you say to your wife while looking at her -- even when it's for the benefit of the counselor.)
Long-term, it sounds like anti-depressants might be of great value for your wife. But as Screwtape, Lsuoma and others have mentioned, SSRIs can initially increase the likelihood of a suicide attempt. So, it might be better were she under professional supervision.
Sorry, man, this sucks beyond belief. But all your efforts so far have not panned out, so another course of action is probably required.