Can Atheists have morals?
Short answer, yes. And we do.
I have to admit, I don't understand - even having been in that world - how people can say someone without religion can't have morals. Christianity has only been around, at most, two thousand or so years. If you pick the various councils, or the conversion of the Roman emperor as the start date, it's less than that. Plus, of course, Christianity didn't spread to the entire world right away (and still hasn't.)
So claiming that without Christianity you can't have morals is just insular, arrogant, and somewhat short-sighted. Did the greeks (from where we get some of our ideals) not have morals? Or the Egyptians? Or the Chinese, one of the oldest extant civilizations?
Now, that's not to say their morals were the same as ours. You can't even say everyone today, even in the same country, state, city, or belief system, have the same morals. Some look at divorce or gay relationships as immoral, others see the denial and repression of those people, or of forcing a couple who really would do better apart to stay together, as immoral. Who is right?
Morality is rarely black and white. It's part of why we have multiple definitions for things, even that should "at first glance" be considered cut and dry. It's why we have suicide versus "self-sacrifice" - someone cutting their wrists out of depression and dying and someone jumping on a grenade to save their friends, fellow soldiers or family are both just as dead, and both made the decision to take an action to kill themselves - yet one is a sad loss, the other, while still sad, is seen as noble and heroic.
What makes one "better" than the other? The intent and the result. And this, to me, is the key to what morals are.
What does morality do? It gives us a guide that lets us live together - as a family, as a culture, a tribe, a nation. A deity can be created to "hand down" those morals, but it's really not needed. Murder, for instance - the killing of another person, not in self defense or defense of family or nation - is generally seen as wrong. (I say generally because, even here, we hit shades of grey - we in the West see "honor killings" as wrong, for the most part, while other cultures see it as right, if not a duty, to restore family or personal honor. But while it is murder, they don't consider it murder... part of what makes this discussion both difficult and contentious.)
And morality both changes through time, and gives an insight into a culture. For instance, rape is wrong. Rape is immoral. It's an absolute violation of someone. Today, people go to jail for it. Yet, in the bible, the restitution for rape is... that the rapist can marry his victim. (Talk about torture for the victim.) Why? At that point, women were, essentially, property. Raping that woman damaged another man's property and lowered her value - so the rapist made up for it by basically buying the property, with as little emotion as if someone ran into a car and had their insurance pay the damages. Today, most of us would see that as absolutely sickening.
So, the Christian's question, typically, is "without God, where do you get your morals?"
I can only answer this for myself, of course. But my secular morality can often be boiled down to "Does this make things better for someone else, or hurt them? Does it aid society in making it better, making it easier for us to get along, and/or treat each other equally or not?" If it improves the general welfare, even if it doesn't make my personal life easier, it's usually "good" or "moral." (Not to mention legal.)
This is why I don't steal, for instance. Sure, I could steal groceries (theoretically) and feed myself at a fraction of the cost it does now. It would be personally advantageous. But the result is that the grocer loses money, not just directly through the loss, but through replacing it, through time spent finding out who did it, possibly by hiring more security or installing security systems, and if enough people did it (and he or she didn't go out of business) by raising prices on everyone. It's a loss as a whole. (Even ignoring my own risk of jail time.) It's bad for the community as a whole. It brings everyone down.
This is also why I support things like same sex marriage. Denying a loving couple the same right as a mixed-gender couple to publicly acknowledge their relationship and get the benefits (and responsibilities) of it makes them second-class citizens. It makes them "less than" everyone else. This is not fair or right, and to me, needs fixing - especially since every argument against it is either illogical, fearful, ill-informed and/ or religious, versus factual, in nature.
So, yes. Atheists do have morality. We don't become lawless creatures just because we have no deity we worship.