These are not the only yarn businesses in Ireland but these are the yarn businesses in Ireland that have Ravelry groups associated with them.
Crafty Knit & Stitch; are a group of knitters and stitchers who meet at The Crafty Alley Shop in Killarney, Co. Kerry every Friday morning from 10am to 12pm. No charge just pop along to meet other people with your needles and yarns.
Clashee; Clasheen; is a rural retreat in the Southeast of Ireland and concentrates on feltmaking
Vibes and Scribes is a bookshop and knitting shop in Cork and I have a sneaking suspicion that I'll never be allowed to visit because that much of my hobbies in one place might lead to a world implosion event.
The Spinning Wheel is a group for a shop in Trim, Co Meath
This is Knit a great yarn shop in Dublin City Centre, website here
The Constant Knitter is a mostly internet business but you can ring ahead to visit website here
JWS Knittersis a group for a Belfast based Shop
Dublin Dye Company - they dye yarn in Dublin, it's sold mostly in This is Knit,
LHogan Wool Fiber, she dyes amazing roving and occasional handspun, her etsy shop is here