Good question! It sounds like you're somewhat familiar with how the banjo (or the instrument(s) that prefigure it) made its way to the United States, primarily through slaves. The instrument, and its playing style, developed from something much closer to claw-hammer style (5 string), to four string tenor banjos, and 5 string "scruggs" style playing. It is from this second type of instrument, the tenor banjo, that banjo made its way towards Ireland.

Unlike 5 string banjos, or earlier minstrel and gourd style banjos, a tenor banjo has four strings and is tuned in fourths, the same as mandolin and violin. This instrument came to prominence in the 1920's and 30's in American jazz music. Once you listen for it, you can hear it in many classic jazz standards from that time period. It wasn't until the 1950's and 60's, during the folk revivalist movement, that the tenor banjo, along with the guitar and a few other instruments, made their way into the standard repertoire of Irish folk music. A huge chunk of the popularity of tenor banjo in Irish folk music can be attributed to Barney Mckenna, of the Chieftans, and more famously the Dubliners. So in short, the tenor banjo becoming a staple of traditional Irish music is actually quite recent, and is a direct product of the folk revival movement of the 50's and 60's.