I'm having the hardest time finding lodging in Kilkenny for a Sunday and Monday night in early June. Every place I've contacted has come back responding they are full, including Michele's earlier recommendation for Alcantra.
If you are trying to book in that first weekend, June 3 & 4, that is a Bank Holiday weekend. If you have exhausted all avenues for B&Bs in Kilkenny, Butler's court, Rosquil House, Berkley House, etc, you might consider looking to the smaller villages & towns close to Kilkenny such as Freshford, Inistioge, Urlingford, Kells or Callan. One of my favorites in Freshford is Pomadora House. I also am a huge fan of Lawcus Farm Guesthouse, which is situated between Kells & Stonyford.
Good Luck and I know it will all turn out splendid! Have a most excellent adventure!
I have a feeling it is the Bank Holiday and Kilkenny would be full up for that. Try Auburndale: http://homepage.eircom.net/~auburndale/ Have you checked at Laragh House?