Conn Progenitor of the Cuinn and Quinn surname

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Conn Cétchathach , or Conn of the Hundred Battles, a son of Fedlimid Rechtmar, was a High King of Ireland and founder of the Connachta dynasty. The Connachta are a group of medieval Irish dynasties who claimed descent from the legendary High King Conn Cétchathach. The modern western province of Connacht (Irish Cúige Chonnacht, province, literally "fifth", of the Connachta) takes its name from them, although the territories of the Connachta also included at various times, parts of southern and western Ulster and northern Leinster. Their traditional capital was Cruachan in modern Rathcroghan, County Roscommon. 

Conn was eventually killed by Tipraite Tírech, king of the Ulaid, on Tuesday 20 October according to Ruaidhrí Ó Flaithbheartaigh in his 'Ogygia: seu Rerum Hibernicarum Chronologia'. The Lebor Gabála, Baile in Scáil, Gilla Cóemáin's poem "Annalad annall uile", Fland Mainistrech's poem "Rig Themra dia tesband tnú" in the Book of Leinster and the Annals where they all report Tipraite defeated him in battle in Túath Amrois. Keating, and the Great Book of Lecan report Tipraite sent fifty warriors dressed as women from Emain Macha to kill him at Tara. "The decision as to Cormac’s sword" says Conn was killed with a sword that once belonged to Cú Chulainn. "Cath Maighe Léna" states that the name of the hill where Conn was killed was Druim Tuirléime. His son-in-law Conaire Cóem succeeded him as High King and Conn's son Art would later succeed him. The Lebor Gabála synchronises Conn's reign with that of the Roman emperor Marcus Aurelius 161–180 CE. The chronology of Geoffrey Keating's Foras Feasa ar Éirinn dates his reign to 116–136 CE with that of the Annals of the Four Masters to 122–157 CE.

So again, pick your timeframe.

I feel it is safe to say that Conn lived during the period of Roman occupation of the whole of Britain.

Roman Britain was the territory that became the Roman province of Britannia after the Roman conquest of Britain, consisting of a large part of the island of Great Britain, less the Scot's associated and affilated with Conn. The occupation lasted nearly 400 years from 43 CE to 410 CE.Julius Caesar invaded Britain in 55 and 54 BCE as part of his Gallic Wars. According to Caesar, the Britons had been overrun or culturally assimilated by the Belgae Celts during the British Iron Age and had been aiding Caesar's enemies. Allegedly, the Belgae were the only Celtic tribe to cross the sea into Britain, for to all other Celtic tribes this land was unknown. He received tribute, installed the friendly king Mandubracius over the Trinovantes, and returned to Gaul. Planned invasions under Augustus were called off in 34, 27, and 25 BCE. In 40 CE, Caligula assembled 200,000 men at the Channel on the continent, only to have them gather seashells (musculi) according to Suetonius, perhaps as a symbolic gesture to proclaim Caligula's victory over the sea. 

Three years later, Claudius directed four legions to invade Britain and restore the exiled king Verica over the Atrebates. The Romans defeated the Catuvellauni, and then organized their conquests as the province of Britain. By 47 CE, the Romans held the lands southeast of the Fosse Way. Control over Wales was delayed by reverses and the effects of Boudica's uprising, but the Romans expanded steadily northwards.
The conquest of Britain continued under command of Gnaeus Julius Agricola 77–84 CE, who expanded the Roman Empire as far as Caledonia. In mid-84 CE, Agricola faced the armies of the Caledonians, led by Calgacus, at the Battle of Mons Graupius. Battle casualties were estimated by Tacitus to be upwards of 10,000 on the Caledonian side and about 360 on the Roman side. The bloodbath at Mons Graupius concluded the forty-year conquest of Britain, a period that possibly saw between 100,000 and 250,000 Britons killed. In the context of pre-industrial warfare and of a total population of Britain of c. 2 million, these are very high figures.Under the 2nd-century emperors Hadrian and Antoninus Pius, two walls were built to defend the Roman province from the Caledonians, whose realms in the Scottish Highlands were never controlled. 

Around 197 CE, the Severan Reforms divided Britain into two provinces: Britannia Superior and Britannia Inferior. During the Diocletian Reforms, at the end of the 3rd century, Britannia was divided into four provinces under the direction of a vicarius, who administered the Diocese of the Britains. A fifth province, Valentia, is attested in the later 4th century. For much of the later period of the Roman occupation, Britannia was subject to barbarian invasions and often came under the control of imperial usurpers and imperial pretenders. The final Roman withdrawal from Britain occurred around 410 CE; the native kingdoms are considered to have formed Sub-Roman Britain after that.

Following the conquest of the Britons, a distinctive Romano-British culture emerged as the Romans introduced improved agriculture, urban planning, industrial production, and architecture. The Roman goddess Britannia became the female personification of Britain. After the initial invasions, Roman historians generally only mention Britain in passing. Thus, most present knowledge derives from archaeological investigations and occasional epigraphic evidence lauding the Britannic achievements of an emperor. Roman citizens settled in Britain from many parts of the Empire.