Rugby (Union, League, Sevens, Womens )- Ireland (32 county), Boxing - Ireland (32 county), Hockey - Ireland (32 county), Athletics - Ireland (32 county), Tennis - Ireland (32 county), Motor-sport (A1 GP) - Team Ireland, etc. etc.
Atheltics - GB and Northern Ireland team? IOC events are separate, Ireland competes as Ireland.
Golf - Harrington Ireland, Clarke Northern Ireland...
It was a FIFA problem because it doesn't exist for any other sport, whether competing across 32 counties or not. It was a FIFA solution because their response was to make a country play under a different name. Northern Ireland is Norther Ireland, Ireland is not the Republic of Ireland. The correct response would have been to respect a country's constitution. Though I suspect it was because there aren't enough references to hot pants in the constitution.