Ralph, Thank you for your research. I've made some progress since I posted my request on this forum. The John O'Malley in 1875 could be my grandfather who was born April 4, 1875. I found that my grandmother's name was spelled Conniely. I put what I found about my family history on a website www.bomalley.net.
I'll take your advice and will register for Irish Family History Foundation's database.