Probably from the 1970's or earlier. The general background is that humans have become powerful on the order of God and Satan. Humans attack God, and perhaps with the help of Satan, God is destroyed. This leads to a period where daemons run amok (don't they always?) on the Earth, but gradually the daemons' behaviour becomes more constrained. Something is controlling and limiting them. There are rumours that God, contrary to reports, is not dead. But, it turns out that Satan, realising that he is now in charge instead of being the competition, has to run the world properly - and is, in effect, becoming God.
In the first book, an arms dealer hires a black magic magician to release all the demons from Hell for a night, and at the end, one of the most powerful demons announces that they cannot be made to return because God is dead. In the second book, the demons are more restrained and hints that God may still be alive.
Satan indicates he may be more fit than any other to take God’s place but it turns out he cannot.
Sounds like it might be James Blish's Black Easter and its sequel, The Day After Judgment, later released as a single volume, The Devil's Day, first published in Galaxy Magazine, August–September 1970, available at the Internet Archive.
In the first book, a wealthy arms manufacturer, Dr. Baines, comes to a black magician, Theron Ware. Initially Baines tests Ware's credentials by asking for two people to be killed, first the Governor of California, Rogan (Reagan was governor at the time of writing) and then a rival physicist. When this is accomplished to Baines' satisfaction, Baines reveals his real reason: he wishes to release all the demons from Hell on Earth for one night to see what might happen. The book includes a lengthy description of the summoning ritual and a detailed (and as accurate as possible, given the available literature) description of the grotesque figures of the demons as they appear. Tension between white magicians (who appear to have a line of communications with the unfallen host in Heaven) and Ware is woven over the terms and conditions of a magical covenant that is designed to provide for observers and limitations. Black Easter ends with Baphomet announcing to the participants that the demons can not be compelled to return to Hell: the war is over and God is dead.
The Day After Judgement, which follows in the series, develops and extends the characters from the first book. It suggests that God may not be dead, or that demons may not be inherently self-destructive, as something appears to be restraining the actions of the demons upon Earth. In a lengthy Miltonian speech at the end of the novel, Satan Mekratrig explains that, compared to humans, demons are good, and that if perhaps God has withdrawn Himself, then Satan beyond all others was qualified to take His place and, if anything, would be a more just god. However, the defeat of Satan is complete. He cannot take up this throne and must hand the burning keys to man, as this is the most fell of all his fell damnations. He never wanted to be God at all, and so having won all, all has he lost.
Found with a search for novel "god is dead" devil demons.
Quotes from user14111's deleted answer:
The Fall of God put Theron Ware in a peculiarly unenviable position, though he was hardly alone. After all, he had caused it—insofar as an event so gigantic could be said to have had any cause but the First. And as a black magician he knew better than to expect any gratitude from the victor.
Nor, on the other hand, would it do him the slightest good to maintain that he had loosed the forty-eight suffragen demons upon the world only at the behest of a client. Hell was an incombustible Alexandrine library of such evasions—and besides, even had he had a perfect plea of innocence, there was no longer any such thing as justice anywhere. The Judger was dead.
Now at last, the great wings stirred slightly, and then, the three faces spoke. There was no audible voice, but as the vast lips moved, the words formed in their minds, like sparks crawling along logs in a dying fire.
[. . . .]
That vacuous space where once Eternall Good
Had dwelt demanded to be filled. Though God
Be dead, His Throne remains. And so below
As 'twas above, last shall be first, and Wee,
Who by the Essenes' rule are qualified
Beyond all remaining others, must become
In all protesting agonie—the chief
Of powers for Good in all the Universe
Uncircumscribed; but let yee not forget,
Already Good compared to such as thee,
Whose evill remains will'd!
[. . . .]
For ever. Man, O Man, I beg of you,
Take, O take from mee this Cup away!
I cannot bear it. You, and onely you.
You alone, alone can God become,
As always He intended. This downfall
Our mutual Armageddon here below
Is punishment dire enough, but for your Kinde
A worse awaits; for you must rear yourselves
As ready for the Resurrection. I
Have slammed that door behind; yours is to come.
On that far future Day. I shall be there,
The burning Keys to put into your hands.
I, SATAN MEKRATIG, can no longer bear
This deepest, last and bitterest of all
My fell damnations: That at last I know
I never wanted to be God at all;
And so, by winning all, All have I lost.