Atheists often object to christianity and other religions because they believe that if a all powerful and all good God existed he would not allow such suffering in the world. I contend that not only does the Christian model do more to explain the suffering in the world than Atheism, but it also explains suffering better than any other religious view, and here is why: we all desire that the suffering on earth is not only some day taken away and gotten rid of of, but also that there is some purpose or reason for that suffering.
Now, this right off the bat rules out that Atheism gives a good explanation for the suffering in the world, because there can be no reason for it. The world just is the way it is and that sucks. We each desire that there is a reason for the suffering or an eventual end to the suffering, but there isn’t an end or a reason for it nor hope that it shall end. Atheism simply says ‘you don’t like it? Well too bad. That’s just the way it is.’
Other religions do a step better, or at least try. In one way or another most religions give a hope for the end of all suffering. Islam has a heaven in which suffering will end. Buddhism believes the suffering itself is an illusion, but we will one day escape that suffering and the illusion to true reality. Hinduism perhaps has the hardest time, in that it gives no real hope to escape all suffering, but only that you will escape most suffering as you reincarnate to better and better life forms.
Even these religions hopes of the end of suffering fall short in various ways. In Islam one could live a great life and eventually reach heaven, but there is not guarantee that one will reach heaven even if your good deeds outweigh your bad deeds. Buddhism says that you will escape suffering because this world is an illusion and therefore suffering won’t exist in the real one. But if suffering doesn’t actually exist, why should we believe joy, relationships, or happiness exist either? All of those things are actually a part of the illusion that we are trying to escape, so why shouldn’t they also not exist in the real world? As said earlier, with Hinduism we have no reason to believe we should escape all suffering. Furthermore, one may escape it for one lifetime and as a result of how they live that life they experience suffering in the next. Whatever level of escape of suffering one gets in Hinduism in one life does not give a guarantee that you will escape it in the next one. There is no final end to suffering then.
Christianity on the other hand take two large steps forward. First, instead of attempting to eradicate suffering it ends it completely, this world will end and a new one will be brought in which suffering does not exist anymore. Second, where no other religion has even tried to give a purpose for our earthly suffering Christianity gives a justification. God has put us through this life in order to shape and mold us into the creation that he desires us to be. In the end that molding allows us to be the rulers of the new creation in the way that we need to be. Our suffering has been long and hard, but it was not without purpose. In the context of eternity our suffering will feel like a pinprick on the timeline of eternity, and that pinprick was needed to make us into who we needed to be.
BEARDED DISCIPLE 
Yeah, but also judgement and grace. Atheists conveniently seem to forget that it’s us -humans- causing all this suffering to each other. Thomas stabs Jeffery and the atheist blames God? I don’t think so.
God is patient. He will give you all the rope you need to hang yourself, while also always giving you the chance to change. If I knew my son would be a saved man at 63, I wouldn’t want him to die for his actions at 16.
Why does blessing your enemies place burning coals on their head? It’s not so you can find a secret way to revel in their destruction. It’s so you can be as patient and loving as God, giving them every opportunity, for as long as they live, to change. And THAT places burning coals on their heads.
You say that atheism can’t give a “good explanation for suffering, but you indicate that they can give a good, i.e., accurate description of reality: suffering exists, and it sucks (many don’t like it).
This indicates that you mean “good explanation” in a different sense, presumably in the sense of false hope. Yes, atheism doesn’t engage in the wishful thinking that theism often does.