You dont need to camp in Ireland, there is an excellent system of tourist hostels. You can also use the hostels as a base for day rides.
The weather can vary from warm and dry to quite cool and wet, esp in the moutains.
You need something for the pub and for cooler evenings.
2 small/med panniers and a bar bag should suffice.
Drying is not always quick so I take 2 shorts and 1pr padded underwear.
Lightweight waterproof top and bottoms
1 short jersey
one long jersey
tights/tracksters/leggings
ultralight windproof top
1 wicking T shirt
2 quick-dry underwear
1 polycotton travel pants (esp with zip-off legs)
1 warm pullover/light fleece
1 woolly hat or long neckwarmer.
3-4 socks
Travel towel
There are some decent bike shops around so you dont need spare tyres but a couple of spare inner tubes are essential.
You can buy stuff in Ireland if you forget.