Uh, oh... I see that the database has the Latin lyrics worng, so I guess I'd better submit a correction. At least the database doesn't call it "Adeste Fidelis," mixing it up with the U.S. Marines.
The Latin lyrics for the first verse are:
Venite, venite in Bethlehem;
Natum videte regem angelorum.
Venite adoremus! Venite adoremus!
Venite adoremus Dominum.
The Shorter New Oxford Book of Carols says, "The complex origins of both the words and tune of this universally loved hymn for Christmas Day lie in English Catholic circles of the 1740's. It survives in different versions in several manuscripts copied by John Francis Wade."
Some very credible sources attribute the lyrics to Wade himself. The source of the tune is unknown - it first appeared in a document dated 1782, "An Essay on the Church Plain Chant." In 1841, a London Anglican clergyman, Frederick Oakeley, wrote a translation that began with the line, "Ye faithful, approach ye." After converting to Roman Catholicism, he changed the poem to a new form, "O Come All Ye Faithful," and published it in 1852.
The Shorter New Oxford Book of Carols
The Hymnal 1940 Companion (Protestant Episcopal Church in the U.S.A.)
The Christmas Carol Reader (William Studwell, 1995)
Sorry, no Irish origins. It's interesting to see that hymns were being written in Latin in relatively recent times, long after Latin had become a "dead language."