We have been camping in Ireland twice, once with okay on and off weather (some stunning days) and once where it rained pretty much solidly for a fortnight. It is definitely hit and miss.
It was a fair few years ago now but we didn't have any problem finding space on sites. We might have rung ahead as we drove places, but we definitely didn't book far in advance.
On both occasions we used this site:
www.camping-ireland.ie/
They used to send you a booklet, but now you can download a free app. I don't know whether this is a comprehensive list of all sites in Ireland, but it certainly has quite a few.
The thing we found was a lack of sites that allowed campfires, so if that is your thing, you might want to look at this list:
www.lovecamping.co.uk/campsites/europe/ireland/filter_fire
Finally, I found this list of "cool" campsites, that might be helpful.
poloconghaile.com/10-best-cool-irish-campsites/
Obviously bring full wet weather gear with you. Depending when and where you go, there are midges in Ireland, north west mainly I think, the same as in Scotland. Bring Avon Skin So Soft, or your own choice of midge repellant, otherwise you will be plagued. We had them in Galway and Donegal but they may be elsewhere too.
I would recommend, Clifden in Galway, if your journey takes you there.
When we camped in Ireland, we had no children so spent most of our evenings in the pub, keeping warm and dry and enjoying the music etc. If you do have children you will need to think about where you will spend your evenings, if the weather isn't great. An electric heater for an awning may be your friend for the cooler evenings.
Have fun though - Ireland is spectacularly beautiful - greener in the south and then more rugged with some amazing beaches further north. Also if you enjoy surfing, Lahinch seems to be the place the surfers hang out in Ireland.