AIB and several other banks offer Visa cards, both credit and debit. Visa on their side have an "offers" system which you need to sign up for. It's worth taking the two or three minutes to register with the site, as the offers can be really useful.
I got the above from AIB Visa Offers last night and it makes me very happy.
Because I got a €5 rebate for my weekly grocery shopping that I was going to do anyway simply by paying with my Visa instead of my Mastercard, that's why! (I also still got a couple of discounts from Dunnes as I had their discount coupons from the previous week's shopping).
It's worth signing up for the Visa Offers thing if you haven't already.