Cook up a few of your own and divert the conversation to you. Rest assured they only want to talk about themselves, and will quit coming to you.
Caution: your problem will shift to other workers who's productivity will wane, so maybe you should be the shoulder after all.
Chuckles aside, my answer is to remain firmly in an offensive stance. You're there for project success, and expect others to be there for the same. Be honest in your response and point the conversation to impacts to the project. Though empathy is essential, it needs to be exhibited in terms of project challenges. You're not there as a personal counselor. They need to find outside solutions to personal problems. And if the adverse impact to the project of personal problems persist, you need to take corrective action as a project manager.