Depends what you count. Note that I'm speaking entirely of Roman tradition, not any actual history; things before Punic 2 are very dodgy - no Roman wrote history before Fabius Pictor (fl. 3rd c. BCE), and nothing close to a complete Roman history of any sort survives until Sallust, whose in tact surviving works are monographs of relatively recent history.

Most of our surviving information about Rome's past before Punic 2 comes out of Livy, who was born sometime between the 60s and the 50s BCE. When he's writing is under Augustus, after the Civil Wars, and that is problematic. He might be projecting concerns and themes of his own time into the past. He did have sources available: historians going back to Pictor, but potentially even older temple records that would have recorded religious events and potentially other things. He likes to give lists of these events that happen in a given year, and many people assume these lists come from the temple records, but no records survive to make the comparison.

Now, Ti. Gracchus was killed in 133. In tradition the Republic was established in 509. That's 380 years. These were not free of what we might consider political violence. Almost as soon as Brutus expelled the kings (not killed - an important distinction), L. Brutus' two sons became involved in an aristocratic conspiracy to bring them back. The conspiracy was betrayed by letters captured and turned over to consuls (shades of Catiline?), and the conspirators rounded up before they took any action. L. Brutus, as consul, ordered the decapitation of the conspirators including his sons.

In 449 during the rule of the Decemvirate, the decemvir Appius Claudius used a corrupt court procedure to falsely enslave a girl Verginia, whom he lusted for. When her father Verginius lost his appeal he killed his daughter with a knife snatched from a nearby butcher. Verginius cut his way out of the city with his knife and fled to the army, where he inspired a mutiny that became a general Plebeian strike, the first of the Plebeian Secessions. This led to the collapse of the government of the Decemvirate and the establishment of the Tribunes of the Plebs. Appius was charged, I'm not quite sure what for; Livy gives a whole slew of new laws passed but doesn't mention the specific charge. Appointing magistrates without election? The Decemvirs did extend their regime by declaration, but they were granted unlimited powers in the first place. He committed suicide after his arraignment.

Just a few years later, in the late 440s, a guy named Spurius Maelius managed to corner the grain market, and started to give it away to the poor. The Senate feared he was attempting to start a revolution, and appointed Cincinnatus (the famous one) as Dictator. He appointed Ahala as his Master of Horse. Ahala tried to summon Maelius to court - Maelius tried to escape... the summons, I presume? Did Romans have the notion of dodging service? I don't know. Anyway Ahala chased him down and killed him.

That's just in Rome's first 60 or so years. Here's the thing though; that sort of thing we might think of as political violence, but Romans considered it legitimate. Verginius killed his daughter; rare, for sure. There's only one secure act of killing children under the patria potestas attested. But that wasn't the political act; the political act was the general strike that followed. Brutus killing his sons: he was Consul and until the Porcian Laws (maybe 3rd c., it's murky) that was a legitimate power of the magistrate. Ahala killed under the emergency condition that the Senate had appointed a dictator. Perfectly legitimate.

Ti. Gracchus was killed by a mob of Senators in the 2nd century, possibly after the Porcian Laws had been established, and the mob was incited not by the Consul, who refused to take action in the situation, but by Scipio Nasica, who was for sure Pontifex Maximus, but not a magistrate. This was extra-legal killing. Scipio's role in this made him very unpopular, and the Senate eventually sent him on a series of foreign embassies, on one of which he died.

So, it's really a matter of what you consider political violence. Roman tradition includes a number of violent exchanges, or attempts at violence etc. but if you look at later historians such as Appian, who calls the riot against Gracchus the first of the civil wars, and you consider what Romans thought about the legitimate use of violence, Wikipedia's claim might be defensible.

A brief note on Appian: I didn't address Coriolanus here; I was just giving a few examples. Appian did call Coriolanus'... exile? revolt? the first armed strife before Ti. Gracchus. This is what he says:

This is the only case of armed strife that can be found in the ancient seditions, and this was caused by an exile. The sword was never carried into the assembly, and there was no civil butchery until Tiberius Gracchus....

That's probably the source of Wikipedia's claim.