I had a similar problem recently - tenants next door playing loud music, slamming doors, etc.
As mentioned by other posters, the Gardai have no powers in this area. Theoretically, the County Council has a responsibility, but when you contact them directly, they will maintain that they don't in the realm of domestic cases (only commercial noise cases).
Basically, you have to tak the neighbours/landlord to court, or at least start down that route in the hope that the noise will be ceased before it gets to that stage.
If the house is rented, find out who the landlord is (ask around / write to the PRTB outlining your situation / talk to a friendly guard). Find out the names of the tennants themselves. Send a registered letter to the lanlord and / or the tenants, outlining your concerns, with times/dates and descriptions of what was going on and, importantly, the disturbance it caused you. Also hand deliver the letter to your neighbours and keep a record of this delivery (registered letters are sometimes not picked up by the addressees). State that you have begun court action in respect of the noise and quote the relevant legislation.
Contact the District Court and get all the forms ready to go and proceed with the case if things get no better. In the meantime, build up as much evidence as you can (video / audio recordings will be accepted as far as I know). While all this is going on (this might sound a bit strange), try to keep up civil relations with the neighbours (as in: "I've nothing against you, but I just have to look after myself, sorry to have to do this.") Having real conflict with the neighbours on top of the noise won't do your stress levels any good.
We did all the above and, as soon as we managed to find the landlord and the letters went to him, it put the frighteners up him and he got rid of the tenants.
Sympathies to you on your situation, it's an awful situation to be in. Best of luck with it.