There’s the Problem of Suffering.
Suffering can be encapsulated in homo homini lupus and landslides (after heavy rain usually)
Suffering in the world \implies God doesn’t exist.
Isn’t there a Problem of Happiness?
Happiness can be finely-tuned compliment from your boss or a good meal.
Happiness in the world \implies God exists.
I’ve never found the argument that because the world is full of suffering there is no God very convincing. At best, it seems to count against the idea of a God who cares.
It does seem odd to me that a creator style version of God would design a world to be so specifically cruel, a world where the life model is largely based on predation and suffering. Presumably God could have made beings that survived on sunlight, but instead made a world where most beings have to hunt down each other painfully to eat them, often while they are still alive. That seems odd.
I’m not sure what happiness in the world means. Is it simply the absence of suffering rather than it’s opposite? And does this say anything about a potential God?
I’m not sure that I would compare this to cancer of the testicles or a child riddled with cancer. The problem with happiness is it’s often more like a base line. We probably need something like a problem with euphoria/joy.
Both of your explanations/hypotheses frame the explanation in terms of “God.”
Maybe suffering and happiness are natural outcomes of human evolution.
@Tom_Storm I should’ve been more specific. I refer to the OOO-God, whether He’s compatible with, borrowing from you, the “abundance of suffering.”
This, combined with the colorful descriptions of God’s wishes in some holy books, is responsible for the steady trickle of deconverts. This doesn’t matter numerically though as the flock grows by other means. Fully functional, cancer-free danglers for most men and eager beaver love-vessels. It’s an old strategy. There are other policies that synergize with basic human instincts, with the overall effect of an increase in flock count. So if you’re a quantity over quality theist, there’s very little to worry about.
Holy books + Abundance of suffering \implies No God.
By happiness I refer to the bare necessities and simple pleasures of life. There are people who enjoy these features and they’ve given their status as 
on surveys. This isn’t rocket science; now that would be hard to wrap one’s head around.
Happiness is an issue with atheism. If God exists not, whence cometh happiness? Refer to history or perhaps your family tree to get an idea of what the world would be like if God didn’t exist.
Why, what seems to be the problem with euphoria/joy? Sorry, I don’t understand.
@questioner That’s the atheist’s POV, but think about it, evolution is just a theory.
@MCogito You’ve furnished a description-definition of happiness. I’m seeking an explanation under atheism, if possible.
Jesuit 
You know your Bible well.
Atheism in my view is mostly a preference not an argument. (Of course post hoc justification applies to both theists and atheists) So as a type of atheist, I see no significant connection to suffering or the lack of suffering. The rest of these kinds of arguments for the most part strike me as games. But I’m certainly open to a different perspective. Tell me more about.
Fear Management System doesn’t sound like a game to me. I’ve laid out the problem in the clearest, most logical format possible. Refer back to the OP or my subsequent posts if necessary.
Funny you don’t see the connection. Put simply, omnibenevolence, omnipotence, and suffering are incompatible, but omnibenevolence, omnipotence, and happiness are. This is the crux of the matter, which is to say that atheism is dissonant with reality. Perhaps if you role play it, you’ll see the connection. The dad could be God, you could be human and laughing and your sister could be crying, etc.
Don’t forget, Happiness \implies God exists
“just a theory” is using the word “theory” as we do in common usage (meaning “hunch”), not as it is used in science.
A scientific theory is not “just a theory” but a well-supported set of conclusions based on a good deal of evidence.
here’s a brief video to explain the difference between saying “it’s just a theory” and a scientific theory
That’s a definition of a theory. A theory is still just a theory. Einstein’s relativity is a theory and while it works, it is continually being tested for cracks. It is a theory because a) it has survived many tests and b) its predictions have always come true.
Darwin’s theory of evolution is the biology equivalent of Einstein’s relativity. It hasn’t been falsified, but that doesn’t mean it isn’t just one of many possible theories.
The atheist’s problem is that he’s using a scientific theory on the issue raised in my OP.
Darwin’s theory of evolution by natural selection is a theory to explain the well-established fact of evolution. As Stephen J Gould wrote:
Well, evolution is a theory. It is also a fact. And facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world’s data. Theories are structures of ideas that explain and interpret facts. Facts don’t go away when scientists debate rival theories to explain them. Einstein’s theory of gravitation replaced Newton’s in this century, but apples didn’t suspend themselves in midair, pending the outcome. And humans evolved from ape-like ancestors whether they did so by Darwin’s proposed mechanism or by some other yet to be discovered.
When I say “well-established fact,” it doesn’t mean absolutely certainty. Again Gould:
In science, “fact” can only mean "confirmed to such a degree that it would be perverse to withhold provisional assent.”
I disagree with Gould. These are statements not befitting a scholar of his stature. A physicist wouldn’t have said what he said, except under certain rare circumstances.
A theory is a theory, subject to revision as and when it fails to serve its purpose. The Newton-Einstein tension is a classic example. Both Newton and Einstein developed ideas that went on to become theories.
Darwin had the good sense to call his idea a theory. I’ve yet to see a biology book that has a chapter on The Fact Of Evolution. It’s always Theory Of Evolution.
Returning to the main issue. Yes, evolution is compatible with suffering and happiness, but that doesn’t upgrade evolution to a fact.
Suffering rules out the OOO-God but there’s happiness in the world. Whence this happiness? Just as Hume asked, whence this evil?, when he pondered the OOO-God.
I’ll leave it to others on the thread to decide whether yours or Gould’s is the more credible opinion.
The obvious response to the OP is that the deductions are both invalid.
I can’t make the connection (even allowing for the OOO’s) but let’s leave it. I’ll watch what others make of this.
@T_Clark You could also use your brain.
@Banno Ok. Demonstrate the invalidity then.
Remember the 2 are co-arguments. They inform each other.
@Tom_Storm 
Leaving [it to …] is ok, but that’s not an argument.
As I said, previously, other participants in this thread can decide for themselves, whose opinion is more credible.
That’s a cop out. Why relegate your duty to other people? You made a statement. I refuted it. Now the ball is in your court.
If you cannot see that P⊃Q is invalid, I can’t help you.
It is valid for me. You say it is invalid. Quare/why?
Apologies. I didn’t know the blue text was a link.
Perhaps the following informal argument will clarify.
Premise: Holy books & Suffering
Conclusion: God doesn’t exist
Premise: Happiness
Conclusion: God exists
Nope.
Before you insist others use their brains, it might be a good idea for you to use your own. How is it that god’s existence follows from happiness? Why could we not simply be happy despite god not existing? Indeed, that seems to be the case.
The problem isn’t happiness or suffering. The problem is defining them in ways that make it impossible for them to both exist, when, clearly, they both do.
For me, atheism is just how I’m built. I didn’t choose it, and don’t prefer it. I simply don’t believe.