When exactly do you think Rome failed to make a treaty with Carthage? Rome apparently signed a treaty in 509; possibly renewed several times before Punic 1, signed another after Punic 1 (that's the one that apparently set the Ebro as the border of the spheres of influence), assisted Carthage during the Mercenary War (admittedly a little underhandedly), and signed yet another one after Punic 2.

Rome was very aggressive about the terms they asked for (for instance there was a clause in the treaty following Punic 2 forbidding Carthage to wage war without Rome's permission, which became the casus belli of Punic 3 - seems to me like they built that eventuality in on purpose), and different authors have different opinions about how seriously both sides took the treaties, but by-and-large Rome and Carthage got along peacefully enough, if in a state of cold war.

For instance, Polybius gives us what seem to be the texts of several of the treaties. This is the one he gives for the end of Punic 2:

Carthage was to retain all the cities she formerly possessed in Africa before entering on the last war with Rome, all her former territory, all flocks, herds, slaves, and other property: 2 from that day onward the Carthaginians were to suffer no injury, they were to be governed by their own laws and customs and to receive no garrison. 3 These were the lenient conditions; the others of a contrary kind were as follows: Reparation p505was to be made to the Romans for all acts of injustice committed by the Carthaginians during the truce: prisoners of war and deserters who had fallen into their hands at any date were to be delivered up: they were to surrender their ships of war with the exception of ten triremes, 4 and all their elephants: they were not to make war at all on any nation outside Africa and on no nation in Africa without consulting Rome: 5 they were to restore to King Massanissa, within the boundaries that should subsequently be assigned, all houses, lands, and cities, and other property which had belonged to him or to his ancestors: 7 they were to contribute ten thousand talents in fifty years, paying two hundred Euboic talents each year: 8 finally they were to give as surety a hundred hostages chosen by the Roman general from among their young men between the age of fourteen and thirty.

It turns Carthage into something less than a Roman client state, but it's a treaty.

Did a little bit of hunting. For comparison, this is what Polybius says about the 509 treaty. He thinks he's got the actual Latin text, since he's complaining about the translation. You'll see it's very different in its tone and interests from the post Punic 2 treaty:

I give below as accurate a rendering as I can of this treaty, but the ancient Roman language differs so p55much from the modern that it can only be partially made out, and that after much application, by the most intelligent men. 4 The treaty is more or less as follows: "There is to be friendship between the Romans and their allies and the Carthaginians and their allies on these terms: 5 The Romans and their allies not to sail with long ships beyond the Fair Promontory 6 unless forced by storm or by enemies: it is forbidden to anyone carried beyond it by force to buy or carry away anything beyond what is required for the repair of his ship or for sacrifice, 7 and he must depart within five days. 8 Men coming to trade may conclude no business except in the presence of a herald or town-clerk, 9 and the price of whatever is sold in the presence of such shall be secured to the vendor by the state, if the sale take place in Libya or Sardinia. 10 If any Roman come to the Carthaginian province in Sicily, he shall enjoy equal rights with the others. 11 The Carthaginians shall do no wrong to the peoples of Ardea, Antium, Laurentium, Circeii, Terracina, or any other city of the Latins who are subject to Rome. 12 Touching the Latins who are not subjects, they shall keep their hands off their cities, and if they take any city shall deliver it up to the Romans undamaged. 13 They shall build no fort in the Latin territory. If they enter the land in arms, they shall not pass a night therein."

This one is much more concerned with a) limiting Roman commercial activity in the Mediterranean, and b) keeping Punic colonies out of Latium. You can also see in this treaty Carthage and Rome negotiating on equal terms - they are both responsible for their various allies. If we can believe these are at least a fair representation of the terms, if not the language of the treaties themselves, I at least think we can use them as evidence that Carthage and Rome did try to co-exist and when flashspots happened (Saguntum, for instance), it was because they couldn't agree on what the terms of the treaty meant.

Just for reference, Saguntum was a city in Spain, apparently south of the Ebro, and by 218 a Roman ally. Hannibal destroyed the city, Rome complained because Carthage was not supposed to attack Roman allies. Carthage complained that Rome wasn't supposed to have Saguntum as an ally. That confusion was at least the proximate cause (as Thucydides would say) of the war, if not the ultimate cause.