Gallowglass; medieval infantry replacement, STATS 4/3/1, originally mercenaries, some became powerfull Clans in their own right. head to toe chainmail, conical helmet, shield and long-axe (descended from Danish long axe). Famous for not retreating unlike normal Irish hit-and-run.
Utahjazz's Huscarl is perfect for it. (well if the cross was a celtic one it would be). Basically started as Gaelicised Vikings in the Hebridies.
Kerns; normal Irish warriors called up in the "rising out". Armed with javelins, swords and normaly a buckler or gauntlet. The bulk of Irish troops during the Anglo-Irish wars. Very effective from ambush, less effective in open against pikes etc. Swift. I'd say STATS 3/1/2, ignore move cost of woods and marsh, replace pikemen (who were very rare in Ireland). No ideal graphics out there but Utahjazz's European Swordsman is pretty close. KERN were sometimes mercenary but most were just a levy.
Gailianna; like Irish gaestatae, Naked warrior mercenaries in blue woad from earlier times than the previous two. The choice for those who like the pictish swordsman, but don't think he looks Irish. Now you know it does. By the way the Irish term for a naked warrior translates as "Skyclad"
Fianna; the mythical group became the name for groups like the Degad ("seekers"), Craibh Ria ("royal branch", Cu Cullains red branch knights are a mistranslation of royal branch (Rua/Ria)) and the Naisc Niadh. Who were early orders of knighthood who served the high kings of the Cuiga (Ulaidh, Mumu, Connachta, Laighin, Mead). They were knight in that they were noble warriors sworn before god to serve the king, not that they had heavt armour and warhorses. They fought on foot. Gallic swordsmen or Rohan royal guard graphics might fit.
EDIT: By the way the Gallowglass unit in that thread does look Irish but is probably a heavly armed Bonnacht. Bonnachts were household troops who fought either like Kerns or Gallowglasses, but were neither levies or Mercenaries. Gallowglasses were very nearly always armed with a long-axe. If you see a picture of a Gallowgass armed with a two-handed sword, odds are its a Bonnacht equipped to fight in the same role (Heavy Infantry), mislabeled by someone unaware of the distinction. Many continental pictures of Gallowgalsses or Irish warriors are based on second hand description. Gallowglasses and Bonnacht fighting as Heavy infantry often had a Kern or two to act as squires on the battlefield. In the case of those graphics the guy holding his sword is a Kern. SO if you want to use those graphics rename it a Bonnacht, give it 4/2/2 as stats (although equipped like a Gallowglass, a Bonnacht will still retreat rather than fight to the death like a Gallowglass).
You could use all of the above and take away Pikemen and Knights, Catapults, Trebuchets and longbowmen from the Irish and have the computer fight more like the Gaels!