A semantic clarification, which might make this discussion easier to have:

Guidelines for making decisions about the advisability of an action are called ethics.
The valuations that allow one to develop ethical standards are morals.
For what it's worth, the dictionary (and not just Webster 1913 backs this up.

A person with morals has abstract ideas about what is good and bad, such as "I shouldn't increase entropy" or "I should experience pleasure." A person with ethics understands how these rules apply to lived experience, e.g., "I shouldn't blow up buildings" or "I should frequent raves."

In this system, even a pure hedonist has morals, and if she lives up to her standards, he is ethical as well. Of course, most people who ask if someone is moral are asking if she is moral by their standards.

At this point I depart from my neutral linguistic explanation to enter my own suggestion: atheists can be moral because Judeo-christian morality is, when generalized, successful morality. It can be viewed as a matter of game theory or memetics: some patterns of behavior allow a society to survive and prosper; others cause them to fall apart. Properties like mutual trust, collective security, kindness to one's neighbor, and respect for others' property will allow people to work together and succeed. Thus, society is perfectly capable of arriving at what most of us consider moral behavior.

Note that this is not necessarily an atheist viewpoint! God often promises his people prosperity and success, and in later writings he says that he loves them as well. What better way to express love and help the people he chose (or later, those who chose him) then by explicitly giving them the rules that they'd otherwise have to piece together through trial and error?