Deear Donna,
I know of three Charles O'Brien's born in Limerick in the 1870s. They are listed on the LDS Family Search website. One of my great great uncles was called Charles O'Brien. He was born in Limerick City in 1876. His father was called Charles O'Brien and his mother was Bridget Madigan. So far, I've got the O'Brien's family back to 1821 and the Madigan's back to 1840. Charles O'Brien Snr married Bridget Madigan in Limerick City in 1864. I'd be interested to know if any of this rings a bell. Do you have a marriage cert for Charles O'Brien to Delia Cunningham? It might list what his father's name was. I've got heaps of information on Charles O'Brien's siblings for you if any of the information I've shared matches your records.
Regards,
Michael