Northern or Republic? Northern would have to be Blanchflower based on logic Republic would have to be McCarthy or Hourihane
Technically yes: an englishman who happened to play for the republic of ireland. For me it has to be an actually real irishman so i'd go with Taggart. Just a touch too young to say Blanchflower but i believe his greatness came after he left us.
Paddy McCourt? Ok he only played for us for a short time and was well past his best but I'll never forget that goal against Boro.
But you said best "irish" player, not best irish origin. Probably half the players we've ever had would have some irish origin somewhere down the line.