Hello Joni,
We usually search for people going back to the last century so it is surprising to find someone looking for grandparents in such a recent timeframe.
As most of the genealogy sites online stop their records at about 1920 (for privacy), I'm afraid you will have to do this search the paper trail way.
You will need to apply to the general registrar for a copy of your parents birth certificates.
Contact www.groireland.ie and request. This cert should give you the names of their parents, and an address etc. I'm guessing that if your parents married in 1953 then they could have been born in the 1930's?? or 1920's??/
You will need to try and guess your grandparents year of marriage. To do this you will need to know if your parents were the eldest children in their families or the younger? You will need to apply for your grandparents marriage certificates in order to find out what their fathers' names were. When you have traced back to your grandparents and guessed their dates of birth then hopefully you may find then in the 1911 census.
There are civil registration indexes online up to 1958 at www.familysearch.org but these don't really tell you anything so it's just as well to go the the source from the get go.
Sorry that we can't help you with the search, you will just have to apply for these certs yourself. None of us can do that as it's private family business and not given out by the registrar.
If you have any questions then please feel free to come back to us.
Kind regards,
Anne Dennehy