I'm an atheist and I half-suspect that Tillich is an atheist as well! The 'courage to be' boils down to accepting that there is no ultimate, absolute, given meaning to life. If you don't accept this then you will go on existing in a fog of doubt and uncertainty, resulting in extreme anxiety. But if you accept the uncertain nature of life whole-heartedly then existential anxiety disappears.
This acceptance Tillich seems to equate with accepting God. But an atheist can just see it as accepting life in all its uncertainty! Of course this acceptance could be just another acceptance of a false doctrine - Tillich, indeed, recognises this. So there is slight leap of faith involved in accepting life in this way. But it's pretty minimal, and something an atheist can easily do - although he might worry about having accepted Tillich's God.
I give the work five stars because it explores this acceptance of doubt so well. It actually left me feeling less anxious about me being a doubting, cynical atheist. So it actually strengthened me in my atheism. I'm not sure if Tillich would have liked that result or not!
The book itself is very readable, for a work of existential philosophy. Much easier than Heidegger, and hardy more difficult than reading, say, the pop-philosophy works of Bryan Magee. In fact, it gives some excellent thumb nail sketches of the ideas of leading existentialists like Heidegger, Nietzsche, and Sartre on the issue of the 'anxiety of living'. This includes excellent reviews of some of the leading works of these writers. It inspired me to go seek out some of Sartre's novels, and maybe a few other works.