Individual atheists deny or accept different morals sets as they see fit.
When thinking of atheism and theism, think of it as various government systems compared with anarchy. Political systems such as liberalism and communism have a set of doctrines on politics, economics, rights, property ownership, and so on.
Anarchy, on the other hand, is merely the absence of any kind of government. As such, it's got no rules on who does what, or who owns what. Such rules are up to the people to make. Likewise, atheism is merely the absence of religion, and as such, has no rules.
It's a crude comparison, especially as a country can be based on anarchy, but you get the point. Note that I'm not an anarchist, though.
Either way, you can't found a country on atheism. You can found a country and say that it'll be secular, but that's the closest you get.