Irish pubs seem to be taking over the world, but if they're all like these two, I don't care!
Firstly, The Tara, at Rokin 87-89, used to be a Brit pub (O'Henry's) where I worked, but the new owners bought the restaurant next door and expanded the place into the present premises. They offer a good selection of Irish beers and cider, as well as the usual Dutch options, with excellent food as well. It is an excellent lunchtime or early evening spot, and the layout means that it doesn't get too noisy, even when busy. They do have occasional live music, usually midweek - check out the posters at the door for information.
At the other end of the scale is the tiny Blarney Stone at the bottom of Nieuwendijk. This place looks as though it's been transplanted from Co. Kerry or similar and is one of the friendliest bars in Amsterdam, and that's saying something! There's mainly Irish beer and cider on sale at very reasonable prices, with Dommelsch pils for the locals, and they do a wonderful toasted bacon sandwich in the mornings!