Bernard’s answer is the most likely – you really have to cross your fingers when you go to Ireland, as you could be really unlucky with the weather. The warmest time of the year is July and August, but I do remember very pleasant times in April, May and June. I also remember very rainy times in April, May and June.
Between November and March the weather is quite cold. Though it depends on where you are in the country (please try and not just go to Dublin, try and see another part of the country, such as the Burren in Co. Clare), winters are mild with a minimum temperature that rarely goes below 0*C.
Summer or winter, there is still regular rain all year round. (The Atlantic’s favourite hobby is dumping itself on Ireland).
So, unfortunately the only think I can say is when you book your flight, take it with a pinch of salt and hope it doesn’t rain!
If you weren’t asking about Ireland from a weather point of view, then I’ll just talk a little about what’s actually going on during the year.
Obviously, there’s St. Patrick’s day in March and parades and celebrations go on in every bigger town in Ireland.
In mid-August, there is Puck Fair, in Killorglin, Co. Kerry – the southwest of Ireland. www.puckfair.ie – It is one of Ireland’s oldest festivals. Basically just 3 days of drinking though, and some people love it, others hate it so do your research before you go! (feel free to ask me a question)
Another festival I can think of is the matchmaker’s festival in Lisdoonvarna, Co. Clare. This runs in September. I’m sure if you google it, you can find information about this festival and others.