My memory is a bit fuzzy on this one. As best as I can remember, the protagonist is walking in a forest when he comes across an elderly man sitting alone. The two strike up a conversation, and the elderly man reveals that he is God. I cannot remember the process of how the offer comes about, but the gist of it is that God is tired, and wants to find a successor. He convinces the man to accept the mantle, though IIRC the other man is naturally quite reluctant. I do recall that God tells the man to look within himself for wisdom and understanding after the power transfer. The newly-minted God does so, and when he is finished, he realizes that an eon has passed. The forest around him is long gone, and the man who was God has died and is beyond reach now - the new God can't make the old God take his job back (yes, this is sort of confusing, sorry).
As the the story progresses, we learn that the protagonist too becomes weary of being the almighty after several eternities, and passes on the role to another. At this point, the story (IIRC) takes "snapshots" of life under various incarnations of God. I vividly remember one scene where the person who was chosen to be God is a madman, with sadistic tendencies. The planet is awash with disasters. A devout woman, watching the horrors unfold on her television, grabs her crucifix and prays. This twisted version of God hears her prayers, and responds by subjecting her to his unkind attentions.
I do not recall how the story ends or is resolved.
Publication Timeframe/Other Details
I read this one in a sci-fi magazine or anthology (pretty sure it was a sci-fi mag) in the 1980s. So, the story would be no more recent than that. I don't think it any older than the 1970s.