There are no traditional patterns of Irish kilts; kilts are Scottish, and are not a traditional part of Irish dress. They date only to the Gaelic Revival of the early 20th century. This revival is also responsible for kilts' popularity in other traditionally Celtic countries. Scotland is the only country in the world where tartan kilts are traditional.
The closest equivalent to a kilt in traditional Irish culture is the lein-croich, which is a long tunic in a solid color. Green, saffron and black are all traditional colors for a lein-croich, which is never patterned in tartan as a Scottish kilt is. The earliest Gaelic Revival kilts in Ireland are solid-colored, most commonly in saffron or green. Tartan is a later addition to Irish use of the Scottish kilt.
The most famous tartan associated with modern Ireland is the Ulster tartan, which has been produced since 1956. The Clodagh, O'Farrell and Shaughnessy tartans are also designed with Ireland in mind. All of these tartans are the product of modern fashion designers in the 1960s and 1970s, and are not traditional patterns. Despite their design origins, these tartans are more popular outside of Ireland, particularly in the United States and Scotland.