I can recommend the Garden Room restaurant at the Great Southern Hotel in Killarney. It's a lovely hotel (ivy-covered attractive building) with an equally nice restaurant in the centre of Killarney town right across from the train station. Really nice area. It's a bit expensive though. Anyway, have a look at this link and click on 'dining and lounges'
There's a link to a sample menu which includes a rack of lamb (origination of which is unclear :) )
There's also the restaurant in the Aghadoe Heights Hotel which is a few miles (maybe 3 or so) outside the town. Now that is *beyond* expensive, getting in to the ridiculous. It's located in an outrageously exensive hotel! I've never dined there myself but I hear it's something else. Though it's meant to be very posh so it wouldn't be my type of thing but if you want to go all out and spend a bundle of cash, surrounded by serene poshness it could be the one! The location is fantastic with views of the Killarney lakes. This I know from passing it time and time again on route by bicycle to my ultra-cheap budget hostel accommodation for my baked beans on toast!!! :-)
Problem is I can't remember the names of any regular (i.e. non hotel) restaurants I've eaten in in Killarney. There was a lovely little Italian place I went to a couple of years back, not expensive with a great atmosphere and I can't think of the name of it. I think it was on New Street (??). That's not much help. Sorry.
Failing any of the above, there's a link here to info on Killarney restaurants. you might see something you're interested in.