The story
From Eire + -an. "Éire" is the official Irish-language name of the state under its 1937 Constitution. In the United Kingdom "Eire" was used in English, officially until 1949 and unofficially for decades longer. The adjective "Eirean" was invented accordingly. See names of the Irish state.
Etymology from Wiktionary, CC BY-SA 4.0.