I'm heading over with my wife and two (now in their 20's) daughters at the end of next week. It's only the second time in many trips since 1990 that I've been over there in Autumn. Really looking forward to it.
We likewise went for a month late Sept-most of October in 2016. Weather gods smiled down on us. We have been in Ireland 3 other times in autumn. Also tried Late Mar/early April and August. Best weather was actually Autumn, but August was pretty nice, but too busy and crowded. We would like to try May sometime....soon! Dan
We've never done a may visit -- YET! Aiming to do so in 2019, though.
Mostly June and July visits, but we made a few April trips, as well, in the early '00s. One cold and wet Feb trip, too -- but most years we've been exceedingly lucky with the over-all weather.
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Bob
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I've almost always gone in May. It's a nice time of year for Ireland. Sun is up late and it's not crowded. We've had good luck with weather in May too for the most part. My last time going in September was my first trip there all the way back in 1990 (where has the time gone?!?). It was beautiful. I fell instantly in love with Ireland on that first drive through Connemara.
May is great for all the baby animals bouncing around the fields. More daylight than in Fall, crowds haven't built yet, and the travel industry people seemed refreshed after the winter.
I've done 2 late Sept early October trips now. The crowds are down, weather still decent BUT, many places change their hours 1 October to only being open on the weekends. Just last week I went to 3-4 spots that were closed, but according to the website should have been open even with their modified schedule (Youghal clock tower and Ferns castle stick in my mind).