The Irish intermarried with various ethnic groups. Sometimes to find Irish origins, you have to explore the other group.
For example, in the American Southeast, the Scots-Irish intermarried heavily with the Catawba, Cherokee, Chickasaw, Choctaw and the Muscogee (Creek). If the geography and time period was right for intermarriage, then research tribal records. Remember, tribal membership is determined through a documented lineage. Within that lineage, often in a compiled family history, the Ulster branch may be documented.
The same principle applies to the Maori of New Zealand. They are very mixed-blood with both Catholic and Protestant Irish. Another plus for Maori research is large numbers have converted to Mormonism which almost guarantees additional genealogies.
Even stranger, the Scots-Irish were kidnapped during tribal raids in New England in the mid-1700s, and taken to Quebec. There are entire books written about the kidnapped, their conversion to Catholicism, adoption into the tribes, their native names, and those who eventually returned to New England. Upon returning, they spoke French and a First Nations language (some broken English), finding New England Protestant culture very alien to them.
Sometimes, intermarriage is as simple as an Irish Catholic marrying a German Catholic. In some parts of North America there was hostility between the two groups (example: Cincinnati, Ohio). In other areas, the intermarriage was common place. It may be within a German Catholic record birthplaces in Ireland are preserved.
You will find Scots-Irish Presbyterians marrying German Baptist Brethren (now Church of the Brethren). They settled among each other in the Mid-West and on the frontier in Virginia and Maryland in the mid-1700s. Once you realize your Anabaptist ancestors were really Scots-Irish, with a Germanized surname, this directs your research into Brethren record for an Irish birthplace.
As odd as any of these strategies sound, they do work. This is thinking outside the box.