You have distorted Christianity and so you have distorted its conception of morality. Christianity does not teach that we are either saved/damned on the basis of our behavior. Instead it teaches that 'none are good' and we are only saved through Christ. This does not mean that becoming a Christian will not make one good- it will. However, the connection you have made between behavior and eternal destiny is a creature of your own making.
Furthermore, how can an atheist do good for its own sake? There is no place for good in the atheist universe. If we are the creation of random chemical interactions then I see no basis for of the existence of goodness.