There is no credible evidence that the apostle James ever visited Ireland. According to Acts 12:1-22, James was beheaded in Jerusalem by Herod Agrippa, with no indication that he had traveled. Acts does include passages about other apostles' travels--most notably Paul, but also Philip in Samaria and Peter in Caesarea.
Much later, a legend arose that James had gone to Spain to preach the gospel before returning to Jerusalem to be martyred. And even later--in the 17th century--Spanish chronicler Joseph Pellicer wrote that James had also spent time in Ireland.
Since England had not been invaded by the Romans at this time, and Ireland was beyond that, the odds are extremely unlikely that any such event took place. There are always legends created in far-flung areas of having Biblical 'celebrities' visit, but travel was not easy in those days.
Most evidence says that the James apostles were martyred in the Holy Land.
There doesn't appear to be any evidence that the Biblical Apostle James-(a.k.a. "James The Greater") ever visited Ireland. Such a claim tends to echo the lore behind Joseph of Aramathea-(sp?) visiting Glastonbury, England 2000 years ago-(i.e. The story of the Holy Grail, which is more Monty Python than historical reality). Irish Christianity really originated with Saint Patrick during the 400's AD/CE-(about 350-400 years after Saint James' "martyrdom").
James, very likely visited Spain where he began his proselytizing/missionary work-(though, for the record, there is no verifiable primary historical evidence which proves this). He was reported to have spent much of his time in Northern Spain, though when returning to Jerusalem, he was the 1st Apostle to have been executed/"martyred" in 44 AD/CE. The mixed historical and legendary story was that James' head was buried/encased in Jerusalem-(If my memory is correct, there is either an Armenian or Syrian Church that claims to have the martyred/encased head of Saint James). However, his body was reported to have been transported from Jerusalem, to the Galician coast of Northwest Spain. When Spanish Catholic Monks or Priests discovered the (alleged) body of Saint James 1200 years ago, the Camino Del Santiago/Road of Saint James was born. About 1000 years ago, a Shrine Cathedral was built in the Saint's honor and it is the final destination point for trekkers who walk along the Camino over the past 1000 years-(Saint Francis of Assisi, was one of the earliest historical figures to have walked the Camino Del Santiago). It should be noted that Saint James/"Santiago", is the Patron Saint of Spain and is second only to Saint Peter in terms of Sainthood.
(It should also be noted that James' brother, was John, as in Apocalypse John or Saint John, the Author of the Book of Revelation who spent his later years on Patmos Island in the Aegean and is buried in Ephesus in Western Asia Minor/present-day Turkey).
The story of James, like many early Christian Saints and "Martyrs", is a complex mixture of history and legend. It is often difficult to distinguish the historical reality from the lore-(or to try to distinguish...the indistinguishable). Nevertheless, the mixed history and legend of Saint James has played a central role in certain Christian cultures over the centuries...most notably Spain, though not in Ireland-(to the best of my knowledge).
(Side note: There is an above written statement which says, "The Romans never invaded England. England did not exist." That is both correct and incorrect. It is certainly true that the name, "England", did not exist during the time of the Roman invasion, which dates back to Julius Caesar. But, it is certainly true that the land of Britannia/Britain was invaded by the Romans over 2000 years ago. The name, "England", means, "Land of the Angles". The Angles, were the 1st (or one of the earliest) Germanic tribes who invaded Roman occupied Britannia. However, the majority population living under Roman and early Anglo-Saxon Britannia, were Celts).