There is no doubt that Roman coins were widely used in trade outside the borders of the empire, and over time, and presumably as the result of long series of exchanges, they worked their way to some remarkably distant locations. For example, a Roman coin dating to Trajan’s reign was unearthed 3 feet down and 100 miles inland along the Congo, at the highest point up the river that is navigable by large ships. Others, from the fourth century, were recently discovered in Okinawa, and Byzantine-era coins crop up in some numbers in India and China. There is evidence that such coins could remain in circulation for centuries after they were minted, meaning there was plenty of opportunity for them to travel well outside the Empire.

It's a misapprehension, however, to assume that Celtic peoples did not mint coins. In fact, similar coin finds are some of the best evidence we have for Iron Age trading networks. Two coins minted by Tasciovanus, a British ruler of the Catevellauni in the south-east of England, who died in 5 A.D., have turned up in Denmark, for example.

To answer your question more precisely, there is no evidence of a specifically Manx coinage before the medieval period (c.14th century), and there is some evidence that other tokens – for example annular, glass and amber beads – were used instead; certainly the island was not dependent solely on barter. However, lack of evidence for early minting does not make it absolutely certain that early coins did not exist and, in addition, Man had known trading links with Irish polities such as Leinster, by which Roman coins could have entered the island, and may have traded with Roman Britain direct. At least seven Roman coins have been found on Man; most of these can be seen on display in the Manx Museum in the capital, Douglas, These range from a bronze of Tiberius (14-37 A.D.), minted in Alexandria, to one of Constans (337-350).

Of course this does not take account of the perceived value of money in an economy like the early Manx one. Coins containing previous metals might have been valued, but the imperial sestertius was made of brass and had no obvious intrinsic value to a Manxman. Logically that suggests that while trade may have taken place between Man and Roman Britain, it would have more likely involved payment in gold or silver, or barter, than standard coins.

This said, the island was known – the Romans called in Manavia Insula – and the Manx were seafarers; there is at least one piece of human evidence that some trade probably took place: excavation of a coastal site in the south of the island in the 1970s uncovered the bones of a single adult, carbon dated to 70 A.D. +/-150 years, tentatively identified as the victim of a Roman-era shipwreck.

Sources:

Jefferson's Guide to the Isle of Man (1840) p.104

M.P. Charlesworth. "A Roman imperial coin from Nairobi." The Numismatic Chronicle and Journal of the Royal Numismatic Society 1949

Charles Clay. Currency of the Isle of Man, From Its Earliest Appearance to the Assimilation with the British Coinage in 1840 (1849) p.23

David Moore. The Other British Isles: A History of Shetland, Orkney, the Hebrides, Isle of Man, Anglesey, Scilly, Isle of Wight and the Channel Islands (2011) p.97

Philip Nelson. "Coinage of the Isle of Man." The Numismatic Chronicle 1899

Heather Smith. "Celtic beads from the British Isles" on academia.edu

R. Thomsen, "Ancient British coins found in Denmark." The Numismatic Chronicle 1952