In an Irish pub, traditional wooden stools are a good option to match wooden tables. These can be made of the same type of wood as the tables, such as mahogany or oak, and can have a simple, classic design. Another option could be bar stools with a high backrest and footrest, these can provide a more comfortable seating. Additionally, you can consider using stools with a leather seat and backrest to add a touch of elegance and comfort to the pub.
It's a good idea to have a mix of seating options, including both high and low tables and a variety of seating heights to accommodate different groups. You could also include comfortable leather chairs and booths for a cosy and welcoming atmosphere. Adding in some unique pieces such as vintage or reclaimed seating and tables can also add to the authenticity and character of the pub.