People certainly don't associate the emerald isle with Jews, but joking aside, there has actually been a notable Jewish presence in Ireland. The lord mayor of Belfast at the turn of the 20th century was a Jew, as has been the Lord-Mayor of Dublin on two occasions. A president of Ireland has been of Jewish decent, a president of Israel was born in Belfast, and an area of South Dublin used to be known as "Little Jerusalem."
Legend states that along with his more infamous feat in regard to snakes, St. Patrick chased the Jews out of the Hibernia of his day. This would seem to indicate a Jewish presence on the island before the 6th century, but, although Jews are notoriously well traveled in their diaspora, we must relegate this idea to mere speculation.
The earliest record of Jews in Ireland is in the Annals of Innisfallen from the year 1079, which records the arrival of five Jews from over the sea. It is probable that they came as merchants from Rouen in France. In the late 15th century, there may have also been some settlement along the south coast of Iberian Jews fleeing the Inquisition. The honour of having the first Jewish Mayor in Ireland supposedly goes to the town of Youghal in County Cork, where a William Annyas was elected to that position in 1555!1
The unambiguous history of Jews in Ireland begins in the 1660s. With the British Empire fresh from relaxing its 300 year ban on Jewish residents, a handful of Portuguese descended Jews, by way of the Dutch Republic and other places, settled in Dublin. Thus the first Jews of Ireland, as in America, were Sephardim. A prominent one of these early Jewish Dubliners was Jacob do Porto, from whom Erskine Childers, former president of the Irish Republic, is descended. The first known synagogue in Ireland was founded in 1660, in Dublin.
As major cosmopolitan centers of the British Empire, Dublin and Belfast received immigration from impoverished areas of Eastern Europe at the end of the 19th century, and Jews were well represented in this wave. The concentration of Jewish families along the Ring road in South Dublin became known as "Little Jerusalem" and a Jew, Sir Otto Jaffe, was elected to two terms as Lord-Mayor of Belfast beginning in 1899. Chaim Herzog, a president of Israel in the late 80s and early 90s, was born in Belfast in 1918.
Jews were sufficiently common in Ireland for James Joyce to make the lead character in Ulysses a Jew named Leopold Bloom. However, Ireland was never a major Jewish nation. It is estimated that the Jewish population of the Republic peaked at just over 5000 in 1940, although there may have been quite a few more in Ulster.
Jews have continued with some success in Irish political life. A Jew, Robert Briscoe, was Lord-Mayor of Dublin in 1956 and 1961, his son Ben Briscoe was Lord-Mayor in 1988, and another Jew, Gerald Goldberg, was Lord-Mayor of Cork in 1977. Today there are currently some 1700 self-identified Jews in the Republic, the numbers having diminished over the years by emigration and intermarriage, presumably.
Here's a quote from Michael Davitt in 1904:
"The Jews have never done any injury to Ireland. Like our own race, they have endured a persecution, the records of which will for ever remain a reproach to the 'Christian' nations of Europe. Ireland has no share in this black record. Our country has this proud distinction - freely acknowledged by Jewish writers - of never having resorted to this un-Christian and barbarous treatment of an unfortunate people."
help from http://members.tripod.com/Niallf/Irishjews.htm
1This paragraph contains information claimed on the jewishpeople.net site. I have not independently verified it.