grandparent route is a little more cumbersome...
You need to have Birth/Marriage Certs or request an original / certified copy
http://www.hse.ie/eng/services/list/1/bdm/Certificates/
Takes about 10 days and costs 20 euro per document.
Documentation Requirments
Your Irish-born grandparents details
Original Long form Civil Birth Certificate (plus photocopy)
Original Civil Marriage Certificate (if married) - Church certificates are NOT acceptable (plus photocopy)
Original Divorce Decree (final) if Divorced and Current Civil Marriage Certificate ( if remarried) (plus photocopy)
Declaration of Alienage (if they ever renounced their Irish citizenship)
Certified/Notarized Copy of current passport or identity document (e.g. Driver's Licence)
Original Death Certificate if Deceased (plus photocopy)
Deed poll (if they ever changed their name). Original must be submitted and must have been valid for at least two years (plus photocopy). Two documents showing proof of usage in the newly acquired name - e.g. Bank Statements, Utility Bills that are at least two years old - must also accompany the deed poll.