Irish nobles and kings kept fighting forces that were fairly well equipped (think knights) called the teaghlach - "troops of the household". These were men that the professional soldiers that were given lands, and they were divided into the footmen (archers, slingers, spearmen, and swordsmen) and cavalry (called Marcshluag). Irish cavalry were fast and well armed, while the footmen were mostly lighter infantry (think the Ostmen from kingdom's britannia campaign). These "elite" foot soldiers would probably be light infantry, similar to how the spanish factions and sicily have "elite" light swordsmen. It should also be noted that the cavalry were armed with javelins and, rather than a lance, an overarm spear. These heavier cavalry were accompanied by their Horseboys - Squires that would skirmish with javelins while the Marcshluag fought in melee. These nobles also occasionally fought on foot... therefore, a Dismounted Irish noble unit would be an option.
Another type of troop was the Ceithirne congbala - local Irish warbands that were employed by the kings. Also called Kerns, these were largely unarmored and armed with bows, javelins, slings, or axes. Therefore, several different units could be made from kerns depending on what weapon they are using. They were, however, noted as being very fast. I guess these warbands conditioned themselves well.
After 1167, "english" troops were more common in Irish armies. Kings also used knights, archers, men at arms, and hobilers, similar to those seen in English armies. These forces became hybridized under Irish kings, as they took on more Irish characteristics over time. I actually found a source that said that hobilers actually originated in Ireland, as there is apparently historical evidence of them being used far earlier in Ireland than by English armies. Plus, the name comes from the Irish horse breed.
Gallowglasses were Connacht's "heavy infantry". They were the elite soldiers up until the gunpowder era, and they fought both with large axes (like in the britannia campaign) and with Claymore along with chain mail. I guess this could be represented with two different units - the Gallowglass Swordsman and the Gallowglass Axeman. While originally mercenaries, the Gallowglasses quickly incorporated native Irishmen in their ranks. These were the elite soldier, armed with heavy equipment, armor, and with a high sense of loyalty and morale.
Levied troops were the gairmsluaigh. They were often levied by kings to fight alongside the professional soldiers mentioned above. They likely utilized spears.
Finally, Scotish knights and pikemen were also present in later Irish armies (similar to how the french employed scots). Both lowlanders and highlanders were part of these forces, and they were not well armored (like the scottish highlander pikemen).
Sources:
http://warandgame.com/2008/09/07/armies-in-medieval-ireland/
http://www.albion-swords.com/swords/albion/nextgen/sword-medieval-irish-bastard-xix.htm
http://www.scottishhistory.com/articles/independence/_derived/sourcecontrol_hobelar.htm
http://www.fanaticus.org/DBA/armies/IV58.html