The usual (Christian) justification for suffering/evil in the world created by a benevolent God is freedom of the will. However, the more interesting question is not about the source of evil (which the free will may very well be) but why God chose to create the world such as it is. Why not create a world with freedom of the will, but without suffering? Even assuming that God is bound by logic such combination doesn't seem to be logically impossible: creatures certainly can do good of their own free will. There are two alternatives.

1) God is powerful enough for all practical intents and purposes, enough to be called God, but not omnipotent. He created only the best of all possible worlds (Leibniz). This position is perhaps the most defensible philosophically, it also avoids logical problems with creation of unliftable stones, etc., but it does diminish deity's status and invites unpleasant questions like what limits God (logic only, inert matter, outer chaos, other beings), is there someone/thing more powerful, etc.

Interestingly enough, the original Christian theodicy wasn't free will. St.Augustine says poetically "the canvas of creation requires both the black and the white paint". "Requires" here can be interpreted differently, modern interpretation is to explain the black by the "just punishment" for the original sin, which brings us to Adam and Eve, and back to the free will. But if God is still omnipotent and hence omniscient creating creatures he knew would sin, and then punishing them for it is hardly an improvement.

2) However, Augustine can be read more straightforwardly. Evil is "required" for the perfection of the world just like black paint is required for the perfection of a painting (evil can be interpreted as lack of good rather than something onto itself but that is beside the point). God is immoral, and he is beyond our conception of morality, his notion of perfection is his own. This is much bolder, and similar to Plotinus's position on the existence of the One, the One can not exist because it is "prior to all existence". But it does evoke the unpleasant taste of "ends justify the means". It is one thing to use "God is beyond our logic and comprehension" to get rid of unliftable stones, it is quite another to convince people to worship an immoral perfectionist.

Formally, there is another logical possibility of asserting both morality and omnipotence, but defending the morality of creating a world full of suffering, for a higher purpose perhaps. For example, the suffering only appears bad to us, not to an absolute being in its wisdom. But this simply redefines morality and is only different in phraseology from the Augustine's position. The question is asked in human terms and has to be answered in kind. One is free to argue that God is beyond human logic and/or morality, but it still leaves him immoral as commonly understood.

There does not appear to be a way to square this circle, one has to accept Leibniz's or Augustine's alternative (or both) and deal with the downsides. Option 2) looks more consistent, but it is rarely embraced, at least not openly. Perhaps, for "public relations" reasons it is more attractive to dismiss the question with something like "this is beyond us" or change the subject to the free will.

What are the modern theological positions on the morality/omnipotence in catholisism, protestantism, etc.? Is the question relevant to other religions?