Jonah, Chapter 3, And He Did It Not

"And God saw their works, that they turned from their evil way; and God repented of the evil, that he had said that he would do unto them; and he did it not." Jonah 3:10  

How can  it be that God would need to "repent of evil"?  It's got to be in the wording, or I run into all kinds of snags regarding the unchangeable nature of God (Westminster Catechism Questions 4) then additional tangles while considering determinism and free will. 

As a counterpoint, Numbers 23:19 floats to mind:

"God is not man, that he should lie, or a son of man, that he should change his mind. Has he said, and will he not do it? Or has he spoken, and will he not fulfill it? God a man that he should change his mind?"

Alistair Begg addresses this change briefly in his Jonah series, "Man Overboard,"

"Now, how then are you to understand that? Well, the fact is, loved ones, that there is no ultimate inconsistency between these two modes of expression. Because actually, when God is said to change his mind, it is really an accommodation to us. When God is said to change his mind, matters are being viewed from our human perspective. Because it appears to us that there has been a change in God. But what in fact has actually changed is our human conduct, not God. -Alistair Begg

Jamieson, Fausset, and Brown also weigh in on this issue: "What was really a change in them and in God’s corresponding dealings is, in condescension to human conceptions, represented as a change in God (compare Exo_32:14), who, in His essential righteousness and mercy, changeth not (Num_23:19; 1Sa_15:29; Mal_3:6; Jas_1:17)." 

These perspectives help in part. They answer the chronologically troubling aspect of the question.  However, the entire mystery of why God chooses to "relent" at times and other times not, remains a mystery for the end of this age.

Source: Michele Lesley

 David, clearly a darling of God, was repentant, but their child still died as a consequence of his moral failure. Lot was spared on account of Abraham, though he didn't seem to repent at all. 

In this narrative, it's oddly the pagans who quickly grasp the need for repentance while the seasoned Jew with the inside track bucks the plan.

"So the captain came up to him and said, "How can you stay asleep? Get up! Call on your god! Perhaps your god will give a thought to us so that we will not perish." Jonah 1:6

Later the king of Assyria explains his reasoning of repentance, "Who knows, God may turn [in compassion] and relent and withdraw His burning anger (judgment) so that we will not perish." Jonah 3:9

As mechanical and man-centered as these thoughts seem, they do hope in God's mercy. In both instances, unbelieving men are willing to "try" God out.

Alistair Begg reminds us that sometimes God chooses to change his plan but other times not. Nor should man assume that man's repentance will result in a "change" of God's reaction. The pagans got this right too; they allowed it could make a difference, not that it must.

Begg feels our American culture is too presumptuous in this regard:

"There is no definite indication that their turning in repentance will be accompanied by a divine turning. He says, “But you never know, God may actually respond in this way.” It’s a reminder to us of this: that the repentant have no case to argue for acceptance. And the future well-being of the repentant remains solely dependent on the grace of God.

That’s why I get so tired of people in America here—sorry to say, that makes me an alien again—I get so tired of people in America and in Britain trotting out 2 Chronicles 7:14: “If my people, who are called by my name, will humble themselves and pray and turn from their wicked ways and do this and do this and do this, and then I will hear from heaven and heal their sin and do their land.”[15] And the way that it comes out is this: “If we press Button A, he is duty bound to press Button B.” We have it completely upside down." -"Man Overboard Series," Alistair Begg

God is God, and He is entirely just whatever He chooses to do.  This is why when David and Bathsheba's son dies, David's right response is to go to worship. He accepts God's sovereignty whichever way it falls upon his life:

"And he said, While the child was yet alive, I fasted and wept: for I said, Who can tell whether GOD will be gracious to me, that the child may live?  But now he is dead, wherefore should I fast? can I bring him back again? I shall go to him, but he shall not return to me." 2 Samuel 12:22-23