Thank you Annette. I found the baptism of David through the Dublin City church records: www.irishgenealogy.ie
I also found the baptism for Jilia Buckley through Ancestry.com.
I was hoping to find some earlier family records, but have not come across anything yet. Also, I have not found and siblings for David. This research is for my sister and brother-in-law, as he is an Archer. I have a clear paper trail from Ireland to the present day, but I have not found a beginning of the trail earlier than the baptism of David.