Unfortunately Michael Nolan is a quite common name in the midlands, so there are a number of possible matches on the civil index.
There is a possibility in the extracted records on familysearch, but be aware that these records do not always cover all areas, so there could be other possible matches not included.
Name: Michael Nolan
Birth Date: 31 Mar 1872
Birthplace: Ballylinan, Queens County
Father's Name: Michael Nolan
Mother's Name: Mary Hart
Ref No : 467
Note the location shown is probably the registrars district, and may not mean the town of the same name.
The reference number is the page number from the civil register and you can use this to search for the references needed to order a cert from the GRO. This would give more details (such as place of birth and father's occupation) to enable to check if this is the correct birth.
Shane