Without downplaying Barney's part in any way - the banjo was around in Ireland long before him! Fintan Vallely's Companion to Irish Traditional Music breaks it down to to two phases, basically:

i. introduction via minstrel shows in mid 19 C. Fretless 5-strings. with gut strings.

ii. reinforcement by steel-stringed, fretted 4-strings at the beginning of the 20 C. Rapid incoporation into dance music and ceili bands.

Fintan's book, incidentally, should be most people's basic reference for this sort of question!

Regards