If you know with a fair degree of accuracy when they were born and in which county, that's a good start. If you know something more than the county name you can get closer to determining the parish. My lines are from Galway and Mayo. The Galway male ancestor's record of birth was quite easy to find. The female Galway/Mayo border one I haven't found yet but I know the names of the townland where the family lived when she was a child and the town where her parents are buried based on the American family's records. There are county historical societies that will search the records for a fee.
Before you go to the Irish records, check the LDS site (www.family search.org) There are some Irish records indexed there -- I found the birth record for the brother of my male immigrant ancestor, but not him. I found cousins of my female ancestor but no one from her own family.
Also check the resources of FIANNA to become better acquainted with finding Irish records
http://www.rootsweb.ancestry.com/~fianna/There's a good site maintained by the Irish Times with some helpful tools but no primary VRs.
http://www.ireland.com/ancestor/This is another fee site (fairly cheap) with a lot of records, but not VRs.
http://www.originsnetwork.com/(as an aside, is Edison Park considered west side of Chicago? )