Hello Jenn, how far back do you want to go? Legend has it that Ireland's first kings were descended from the daughters of Hezekiah, a king of Israel, who lost his own life and that of his sons, way back when. You can read about it in the Bible. Apparently Hezekiah's daughters were rescued by a priest, Jeremiah, and eventually found their way to Ireland via a brief sojourn in Egypt, and settled in a place called Tara, the name of one of them, probably the one who married the local king called Fergus.
The stone of Scone, was believed to be the stone on which Jacob laid his head and dreamed of angels ascending and descending a ladder to heaven. Anyway, this same stone was a witness to the coronations of all the kings of Ireland until the stone was taken to Scotland whereupon all the Scottish kings were crowned upon it.
The stone was taken to England by James VI and I, and all the kings and queens of England were crowned upon it, up to Elizabeth II. The stone was in the Coronation throne.
Recently, the stone was returned to Scotland. I wonder who will be the next king/queen, and will they be Scottish?
As for more recent Irish history, the place where all the Births Deaths and Marriages were stored was burned to the ground, and all those records were lost, so you might come to a point from which you cannot proceed.
Good luck in your searching.