Don't know much about Epicurus, but from what I've gathered he doesn't actually qualify as an atheist. He didn't deny the existence of the gods, he merely claimed that the gods don't actually have much to do with human affairs; they don't punish the wicked or reward the just, and the soul does not persist after death. It was only in comparison to medieval Christian theology that he appeared atheist. Besides, this doesn't disprove God. At best it shows that our understanding and definition of God is flawed, and anyone claiming they have a perfect understanding of God has something they're trying to sell you.
This dilemma has fascinated me for years, ever since I heard about it. I first encountered it as the "bad things happen to good people" argument. I think it's interesting, but I don't really have any problem with it. Yes, it's true that those three things - mercy, omnipotence, and allowing evil - cannot be true of God simultaneously. I would put forth, though, that they could be true alternately.
We always discuss God, and most of religion for that matter, in terms of absolutes. Murder is always bad. Except, it's not. There are times when God commanded killing (very recently, if you believe some people), and there are times when killing is the proper action because it prevents a greater harm. God is always just, but then there are times God shows favoritism to one group or individual over another.
When we speak of humans (and yes, I'm aware of the theological problems with comparing mortals to the divine; get over it), we call someone "good" if they are merely bad only 49% of the time. A "charitable" man does not give all his money away, or even give to everyone that asks. On the other side of the coin, someone is regarded a "criminal" after only a single act, regardless of how they lived the rest of their life.
Following this logic, then, why do we assume God must have 100% compassion up-time in order to qualify as "loving and merciful"? Every holy book there is tells us God is a wrathful and vengeful being; if you are to be such, you must set aside compassion at least temporarily.
Why do we require God to be OMNI-potent, as if it were not enough to merely be "incredibly powerful; moreso, in fact, than you can possibly comprehend"? Someone capable of creating the Earth ex nihilo is powerful enough to get my respect without worrying about how heavy a rock he could lift.
I do not believe God to be omnipotent. For that matter, I'm not sure God actually ever tells us that he is; I think that was a later addition by humans attempting to ingratiate themselves to the divine. I do believe God is omni-clement (all-forgiving) and omni-diligere (all-loving). I also believe God is capable of error, or at least of irreversible behavior that causes regret after the fact.
So I would respond to Epicurus that I believe in a loving, merciful God that allows bad things to happen to good people; sometimes because of his choices, sometimes because of his limitations.