Can I apply for a passport in Ireland/Greece while on holiday?

I’m temporarily in Greece but normally live in another country; can I apply for an Irish passport here?

No, you must apply in the country you are normally resident in. You should only apply to the Passport Section at the Irish Embassy in Athens if you reside in Greece, (or Serbia or Albania, the Embassy's secondary accreditations), or in the case of a lost/stolen passport while visiting here.