Not entirely clear what you mean with "externally" accredited.
However as far as I understand any higher education facility that awards officially recognised degrees like MSc and MBA in Ireland needs to have the courses accredited by HETAC http://www.hetac.ie/.
Simply put, if it is not accredited by HETAC than that degree is not worth the paper it is written on - you might as well buy the degree at many of those non-accredited "universities" that flog them.
If it is not an accredited institution, it very much should give prospective students concerns as the degree will usually not get recognised by anyone.
There are some external awarding bodies delivering in Ireland, eg University of Wales. I don't think they would be as highly got as a HETAC Award tbh. Also make sure it's pegged on the European Qualification Framework.
Though you can also find other examples in other degree courses and in other universities of, for example, Financial related degrees being accredited by external Finance organisations. etc, etc