Hello Ellin,
Thanks for your message,
I had a quick look on familysearch.org for records concerning the offspring of Patrick Byrne and Mary McCabe and I found a record for the birth of Rose. On this record her town land/ home place is listed as Rootate.
https://familysearch.org/pal:/MM9.1.1/FGGP-7G3
There is a Patrick and Mary Byrne living in Rootate, Killanny on the 1901 census.
http://www.census.nationalarchives.ie/pages/1901/Louth/Killanny/Rootate/1558983/
You could try searching the 1901 and 1911 census for their children who hadn’t emigrated. You can find them here: http://www.census.nationalarchives.ie/search/
Church and civil records concerning family events like births, deaths and marriages would also help build up knowledge of relations in the area. Most Catholic records are held locally - One site which might be of use is - http://www.irishtimes.com/ancestor/browse/ - where you can ‘browse’ an overview of available records per county. If you have any difficulty, you could try writing to the parish priest for possible assistance.
Civil registration records are available from the General Register Office (GRO). These start from 1864. You can access the website here: http://www.groireland.ie/research.htm
Do you have any other information concerning your cousin Christopher O’Connor? Would you know the names of his parents or any brothers or sisters he might have had? The more detail you can provide, the better the chances of someone recognising your Christopher.
Best regards Michael
Genealogy support.