Honestly, I think we have it a lot easier than the theists in that regard. If someone dings my car, I find that my dog has cancer, or I lose my job, I don’t have to address the problem of evil. I don’t need to figure out how to square the idea of an omnipotent and omnibenevolent god with misfortune. I don’t need to wonder if I am being punished or tested, and I don’t have to worry about prayers that aren’t being answered.

There are multiple non-theistic philosophies and religions that offer a framework for understanding and coping with negative events. Neither Buddhism nor Taoism have an explicit dependency on anything supernatural, especially in the schools and forms most popular in the West. The general idea is that we need to be less attached to certain outcomes and that our suffering arises more from our wanting the world to be how it isn’t.

There’s also a large number of non-theistic schools in Western philosophy that have taken their own various approaches to questions ranging from the meaning of life and the meaning of suffering to how to identify and pursue the good. There’s multiple schools of existentialism, of course, but I would even think that writings on the nature of justice (eg John Rawls, Michael Sandel, Peter Singer), the nature of the ego and human experience (eg Thomas Metzinger), and even works of film and literature can help approach an understanding, which is itself perhaps the best coping mechanism.