I did apply for my student permit outside my country of origin. I am originally from Finland and I was visiting my family in Antigua as a tourist and applied through the High Commission in Trinidad (responsible for Antigua). You just have to be legally in the country you're applying from, in your case Ireland.
As further examples, I had applied successfully in two different countries other than my country of origin (an Asian country) or my country of residence (US):
1. as a tourist in Venezuela and applying to the embassy there in Caracas.
2. as a tourist in Canada (mtl) and applying to Buffalo (already had a history of being in Canada for 5 years previous as a foreign student).