Tentative Irish unit roster subject to project leaders' changes. As with the Welsh, Irish society and warriors were different enough from others that I am unsure of what classifications are best.
~Lught Teaghlach: Lord's retinue and/or bodyguards. Ride small but sturdy Irish horses and are equipped with mail and helmets. They wield spears and swords, and maybe javelins as well. They are the best horsemen of the Irish, and very well motivated as a retinue unit.
~Ridire: The richer members of the general hosting, who can afford horses and good quality armor. They have padded aketons and metal helmets, and can get mail as well. They have the same weapons as the retinue as well but are not as skilled or motivated.
~Horseboys: Squires to the ridires or retinue, they are unarmored and armed with only javelins and maybe an axe for close combat.
~Hobelar: Mercenaries that came about with English influence. Not sure whether to count this as a native Irish unit as most hobelars probably had more modern saddles and fought in the English style, but the horses and maybe some of the soldiers were all recruited from Ireland. They were light cavalry, using spears, that were armored lightly and operated better on rough ground than normal horsemen. They were used by the Scots and English, but possibly by the Irish and Welsh as well, but they are more of the M2TW type of mercenary rather than lordless troops who will fight for a cause like the galloglaich or fianadi.
~Galloglaich: Heavy infantry. Armored in aketons and mail hauberks, with open-faced bascinet helmets and sometimes even metal greaves. They wield a large two-handed axe with great skill, and are rather fearless, preferring death on the field to retreat. They were also known to use bows. Whether there should be a separate archer galloglass unit or give them both axes and bows is up for consideration.
~Cliathairi: Professional Irish soldiers, perhaps the best or closest Gaelic equivalents to sergeants. They are veterans and disciplined to boot. They usually wear padded aketons or reinforced leather for armor, though if you wish you may make them upgradeable to mail. They carry round shields and long spears into combat.
~Fianadi: Heavier Irish footsoldiers, who aren't as disciplined as the Cliathairi but are still able troops, armed with axes, javelins, short swords, and shields, and wearing reinforced leather armor, helmets, and even mail. They are the richer native Irish footmen who operate in mercenary bands that have their own codes of honor and whatnot.
~Ceitherne Congbhala: "Retained Bands", these are the more professional of the kerns, and the best equipped. Some have no armor, but they can get padded or hardened leather vests for protection, and even helmets. They are armed with darts (a lighter form of javelin) and axes and carry a small round shield. Upgraded ones might even carry swords as well, if it's possible to do that. Otherwise just have them have swords as a rarity with most having axes.
~Ceitherne Coille: "Wood kerns", typically considered bandits but can be hired. They are have little to no armor and aren't the most stalwart troops, but their skill with a bow is valuable to Irish armies who have few other archers at all. Beside the bow they rely on a knife for close fighting.
~Ceitherne: Simpler kerns, unarmored save perhaps a hardened leather vest for some, they'd go into battle with a shield and axes or clubs.
~Gairmsluaigh: Levied troops, wielding darts and axes or knives. They are not as tough as ceithernes, and while not simple peasants they are only levied troops forced to fight and becoming increasingly outdated even by Irish standards by the mid-13th Century.