J. W. Wartick has written a nice article evaluating the case for atheistic ethics, particularly as presented by philosopher Louise Anthony. She represents a brand of atheists (such as Sam Harris and Michael Shermer) who refuse the nihilism of an earlier generation of atheists who admitted that if there is no God, there are no objective moral values. She thinks God does not exist but moral values do. Or so she says. When she defines what those moral values are and how they are determined, it becomes clear that they are subjective, not objective. Something has value if she values it, and something is wrong if it causes suffering. But these are mind-dependent, and thus subjective by definition. For meaning and morality to be objective, it must have an existence independent of human thinkers such that even if conscious beings did not exist, moral values and meaning would still exist.
Ultimately, atheists can only put forward various ways that humans can know what is moral (epistemology); they cannot explain what makes those moral values moral. Secular ethics lack an objective foundation.