Transport for Ireland just tweeted that LEAP cards (those green things that save you money up in Dublin) are now working on the Galway City buses (that's Bus Éireann city services and City Direct):

Eagle-eyes here on boards spotted that cards for Galway were available on the LEAP website, and TFI have just confirmed it today after I asked them a few days ago.
I don't know where to buy tickets yet (possibly the outlets are not yet stocked), but if you have a card from Dublin (or Cork where they're just rolling out now, too), then it should work here.
And (guessing) it's possible that driver training here is not yet complete. So be nice to the drivers if they seem a bit confused - this launch has probably happened faster than planned :-)
Don't think they're on any of the regional buses yet, either - though I believe it's coming.
This won't seem like big news to many people. But in Dublin the savings are quite big. And cards like this make transfers, fare capping and lots of other good things possible, and will eventually work nationwide.