Most Scottish tartans were invented in the early to mid-19th century. In the late 19th century a few Irish nationalists started the idea of kilts as a symbol of pan-Celtic identity. It was another hundred years before almost all Irish tartans made their appearance.
One noteable exception is the "Ulster" tartan, which dates from the late 1500s-early 1600s and was discovered by a farmer in the 1950's in the form of a pair of trews which had been buried:

http://www.ulsterscotsagency.com/tartanandkilts.asp

Regards,

Todd