There are just 12 listings for Bermingham in the Kildare online telephone directory and 1 Birmingham.
Narraghmore is about 7 mi. from Kilcullen and one of the Bermingham's lives in Kilcullen. Since it is only 12 I would write them all, stamps are inexpensive genealogy.Postal Codes are not required outside Dublin, addresses sufficient for delivery.

Annette Code

ps was helping someone fairly recently with the same names but not sure if in Kildare. You could try going backwards in dates on the message board a month or so.