I can't think of any aircraft that could make it off Cork's runway and get the whole way to the Gulf. Maybe an ER variant of the 767, but I don't think any Gulf carriers are flying them.
Somewhere with a stop on the way, might make more sense. Emirates have operated to Malta via Cyprus in the past. However, I'm not sure Cyprus is the best location. Even that would be restrictive from an aircraft perspective. Some charters to Cyprus have been known to tech stop on the way because of fuel/weight restrictions out of Cork.
What you need to find is an airport in Italy, Greece, Croatia, Montenegro etc. that can't justify flights to the Gulf on its own, is far enough from a major airport that it has a large catchment and which could also generate some passengers between Cork and that destination. Can't think of too many candidates.