Is there a contradiction between Deuteronomy and Jonah?

Sorry! But this was not a prophecy.
It was a proclamation of doom.The words at Jonah 3:4 only state what Jonah believed was going to happen.Not understanding Gods purpose fully,he believed that he was giving a message of definate destruction.Looking at how God works you have to relate this proclamation to a similar destruction of a city/cities,e.g.that of Sodom and Gomorrah.
If you proved to be righteous you were saved.In fact they were questioning God wether he would destroy the city if a certain number of righteous people were left in it.Lot and his family were the only ones that were not of the debased condition that had taken a firm grasp of the entire inhabitants of Sodom and Gomorrah.Likewise if you repented of your sins then you were saved from Gods destruction, as in the case with the Ninevites.For God to have destroyed them he would have been God that simply destroys for the sake of it.This is what a true prophecy of destruction of Ninevah was like....
Zephaniah 2:13,14 This destruction did happen...13And he will stretch out his hand toward the north, and he will destroy Assyria. And he will make Nineveh a desolate waste,a waterless region like the wilderness.
14And in the midst of her, droves will certainly lie stretched out, all the wild animals of a nation. Both pelican and porcupine will spend the night right among her pillar capitals. A voice will keep singing in the window. There will be devastation at the threshold; for he will certainly lay bare the very wainscoting.Its Destruction Fulfills Prophecy. Although repenting at the preaching of Jonah (Mt 12:41; Lu 11:30,32),the Ninevites relapsed and again took to their wicked ways.It was some years after Assyrian King Sennacherib had been murdered at Nineveh in the house of his god Nisroch (2Ki 19:36,37; Isa 37:37,38) that Nahum (1:1; 2:8—3:19) and Zephaniah (2:13-15) foretold the destruction of that wicked city. Their prophecies were fulfilled when the combined forces of Nabopolassar the king of Babylon and of Cyaxares the Mede besieged and captured Nineveh. The city was evidently subjected to burning, for many Assyrian reliefs show damage or stain from fire and accompanying smoke. With reference to Nineveh, a Babylonian chronicle reports: They carried off the vast booty of the city and the temple (and) [turned] the city into a ruin heap. (Assyrian and Babylonian Chronicles, by A.Grayson, 1975,

Prophecy is an inspired message; a revelation of divine will and purpose or proclamation Prophecy may be an inspired moral teaching, an expression of a divine command or judgment, or a declaration of something to come. Prediction, or foretelling, is not the basic thought conveyed by the root verbs in the original languages (Heb., na va; Gr., prophecy, propheteuo
Basically the word prophecy is applicable only if it is divinally inspired.I originally misunderstood the true meaning of prophecy.I should have known it,or at least verified its true meaning before I posted.(Hasty reply. I was working!)However the word prophecy has a broad meaning and in the case of Jonah it is true "prophecy".Here it is being misrepresented and forced upon the issue to suit,as words to match the words false prophecy in Deutronomy 18:20-22.Deutronomy is referring to false non divinally inspired prophets.Now that I’ve looked at Deutronomy 18:20-22 properly I should have realised that this is referring to false prophets.Those that prophesize of their own back.Those that choose to make others believe that it is divinally inspired. >>Jonah and Jeremiah were divinally inspired<< So the connection with Deutronomy is not applicable.If we break down the Deutronomy 18:20-22 We can see that the context is referring to false prophets...Deutronomy 18:20
"But the prophet who speaks a word presumptuously in My name which I have not commanded him to speak, or which he speaks in the name of other gods, that prophet shall die." ...This is referring to false prophets.Those "presumptuous" ones that have not got Gods authority to prophesise.They only choose to use Gods name.This does not include Jonah and Jeremiah.21 "You may say in your heart, 'How will we know the word which the LORD has not spoken?' ...See last paragraph below.22 "When a prophet speaks in the name of the LORD, if the thing does not come about or come true, that is the thing which the LORD has not spoken. The prophet has spoken it presumptuously...This again is referring to speaking in the name of God only.False prophets have spoken in the name of God but not through divine inspiration of God. Nahum 1:2."Jehovah"is a God exacting exclusive devotion.
Jonah was told to "prophesise" though in Gods name.A warning message to the Ninevites.God was utilising mans free will to serve God.He was initially going to destroy Ninevah,so the "prophecy" was not false,it was merely changed because of their change of heart and that God is a God of love and gave the Ninevites a chance.Testing Prophecy and Its Interpretation:
In view of the activity of false prophets, John warned against believing every inspired expression, which is basically what prophecies are. Instead, he admonished Christians to test the inspired expressions to see whether they originate with God. (1Jo 4:1) John cites one doctrine as a means for determining divine origin of the inspired expression, namely, Christ’s having come in the flesh. Obviously, however, he was not saying that this was the sole criterion but evidently was citing an example of something currently, perhaps predominantly, in dispute then. (1Jo 4:2, 3) A vital factor is the prophecy’s harmony with God’s revealed word and will (De 13:1-5; 18:20-22),and this harmony could not be partial but must be complete for the prophecy or an interpretation of prophecy to be correct.20 But the prophet who speaks a word presumptuously in My name which I have not commanded him to speak, or which he speaks in the name of other gods, that prophet shall die.'
21 "You may say in your heart, 'How will we know the word which the LORD has not spoken?'
22 "When a prophet speaks in the name of the LORD, if the thing does not come about or come true, that is the thing which the LORD has not spoken. The prophet has spoken it presumptuously...(All quotes from NASB)

If you state that Jonah is a false prophet then you are sayng that God is a false prophet,as it was under Gods direction and by Gods wording that Jonah was to deliver the proclamation.Jonah 3:2.."Get up go to the great city and proclaim to her the proclamation that >> i am speaking to you "<< These words did not originate with Jonah.Jonah 3:4 "Only forty days more and Ninevah will be overthrown."Gods words.Nothing new here,God does clean up debased people,but always shows mercy to those that repentMany years later Ninevah was eventually destroyed and by the means of Gods prophecy.Applying false prophet to Jonah,in line with the context in Deutronomy 18:20-22 is incorrect.Deutronomy is a warning to all of us to look out for false prophets.Is God a false prophet? It was God that was prophesying to Ninevah.Jonah was a pawn.Does Jonah really come under the context found in Deutronomy 18:20 "The prophet that presumes to speak in my name a word that i have not commanded him".....Jonah was commanded to speak in Gods name.We must remember that Jonah was frightened.On Gods first command to Jonah,he fled to Tarshish on a boat.This is not a display of an arrogant presumptuous false prophet.If God had not been involved then we would never have heard about Jonah..Jonah didn't want to face up to a whole warrior race of Assyrians.Why would he have chosen to prophesy to such an aggresive people.The Assyrians would skin their captives alive,God hated the practices of the nations outside of the Israelites.The Worshipping of myriads of Gods and sacrificing children to them.
Jonah does not fit the words presumptuous prophet at Deutronomy.Your written premises
Premise 1.God sends a prophecy.
The word prophecy isn't used in the account of Jonah,however,it was a proclamation.Premise 2 God changes his mind. ....
No...The proclamation of destruction of the Ninevites was proclaimed to them.God is always merciful to repentant ones.His intentions of dislplaying his mercy remained constant.Gods display of love overides the proclamation. It was one of the ten commandments from Gods own law.Ex 20:5,6 False gods and displaying love as a premise over everything that was paramount.
"You must not bow down to them nor be induced to serve them, because I Jehovah your God am a God exacting exclusive devotion, bringing punishment for the error of fathers upon sons, upon the third generation and upon the fourth generation, in the case of those who hate me; 6 but exercising loving-kindness toward the thousandth generation in the case of those who love me and keep my commandments".Premise 3.If the prophecy does not come to pass God did not send the prophecy....
Prophecy is basically "inspired expression" from God.God expressed to the Ninevites that they would be overthrown.By understanding Gods will,as one of love,Gods love for his creation comes second only to his expectation that we show devotion to him first.Once that devotion is shown God will then show love and mercy to us (and hence also to the Ninevites)
Although God proclaimed "overthrow",it was only on the basis that the Ninevites would not repent.This is seen throughout the whole context of Jonah .
There is no contradiction,This is not applicable to Deutronomy.God is supreme and he chooses how he will conduct results from his proclamations,but these are always in line with his own laws given to us and through his merciful ways.