There are some forgotten gems like Pierce O'Leary and Paul Byrne, but here are the all-timers. Weak in a couple of positions but here is the all-time Irish players who have played for Celtic.
Packie Bonner
There isn't a lot of competition for this spot. Packie was at Celtic for a whole two decades from 1978 too 1998. His first decade was marked by moderate success by Celtic standards - winning four League titles in an era when Glasgow's supremacy was challenged by Fergie's Aberdeen. His second decade was a grim business altogether as Celtic proved unable to compete with Rangers under Graeme Souness and Walter Smith.
Sean Fallon
A Celtic icon and a former Sligo Gaelic footballer, Fallon began his career at the top - with Longford Town. He coped with the blow of having to leave the midlands and Celtic proved a good fall-back.
The 1950s being a more democratic period in Scottish football, Celtic only one League title (in 1953-54) in Fallon's time as a player.
Mick McCarthy
McCarthy spent just two seasons in the Celtic defence between 1987 and 1989, wrestling the title back from Rangers in his first year. The following year they slumped to third and McCarthy headed for France before things got really depressing.
Darren O'Dea
Strachan brought O'Dea to Celtic in 2006 and and he made a strong impression in his first two seasons, picking up a couple of League titles. He also scored one of the goals in the 2009 League Cup win over Rangers. Became increasingly peripheral in his final two seasons before leaving in 2012.
Chris Morris
The best ever Irish player to share his name with an English comedian, Morris won the Double in his first season in 1987-88 season. Thereafter, there was four seasons of frustration until he left for Middlesbrough in 1992.
Joe Haverty
A little jinking winger who spent most of his career with Arsenal, Haverty played very briefly for Celtic in 1964 before returning to the League of Ireland to play with Shelbourne, Drumcondra, Rovers and Drogheda. He played over 30 times for Ireland over the course of a decade.
Liam Miller
https://www.youtube.com/watch?v=OGvEGpDlfXU
His star burned very brightly during the latter part of the Martin O'Neill era, so brightly that Manchester United plucked him from Celtic after a particularly excellent performance, marked by a goal, against Lyon in the Champions League. He shouls have stayed.
Roy Keane
https://www.youtube.com/watch?v=XVxNxJKTiw8
Only 12 games for Celtic, Strachan barely seemed to want him about the place, Keane's arrival was a great day out for Celtic fans. He picked up a League title but the suspicion remains that it's not his most cherished possession. He did win Man of the Match for the 1-0 win over Rangers in Ibrox.
Aiden McGeady
A Scots-born lad who opted to play for Ireland, McGeady couldn't be any more Celtic if he tried...
Tommy Coyne
A Scots-born lad who played for Ireland, Coyne couldn't be any more Celtic if he tried... Coyne was the Scottish League's top scorer with three different clubs - Dundee United in 1987-88, Celtic in 1990-91 and Motherwell in 1994-95.
His most famous acts in an Irish jersey were scoring the winner in a friendly against Holland in early 1994 and then running so hard in the Giants Stadium against Italy that he collapsed on the team bus the following day from exhaustion.
Robbie Keane
All jokes about boyhood dreams and so forth are banned. And for what it's worth the idea that Robbie dreamt about playing for Celtic as a boy is entirely plausible. Celtic were a mess when he arrived but he still managed a goal ratio of around one a game.