There were 24 Ellen Donnelly registrations 1872/1873, if she was born at the end on 1872 it might have been registered early the following year. You can view the records on the site below, however the 24 were spread over the whole of Ireland, you would need to have some idea of where to look or go through them all. It is an easy site to view once you get used to it but it is free!
https://civilrecords.irishgenealogy.ie
The US census taken after the partition of Ireland
1930
William Kernan, 57, born Irish Free State
Ellen Kernan, 56, born Ireland North
Transcribed Hernan on FamilySearch
Image
https://www.familysearch.org/ark:/61903/3:1:33SQ-GRCN-CV9
1940
William Kernan, 68, born S Ireland
Ellen Kernan, 86(?), born N Ireland
Image
https://www.familysearch.org/ark:/61903/3:1:3QS7-899M-37D8
That narrows Ellen's county of birth to 6 of the 9 counties of the Province of Ulster which became the state of Northern Ireland a century ago.
The counties are Antrim, Armagh, Derry/Londonderry, Fermanagh, Tyrone.
There were several registration districts in each county. Some registration districts crossed county boundaries.
SWilson Info is a useful website for identifying registration districts:
https://www.swilson.info/index.phpSelect topic Registration District Map Browse from menu.
Select a county from alphabetical list and enter it in county box. This will bring up a list of registration districts in that county. Note down list of districts. Repeat for each of the 6 counties. There are between 5 and 10 registration districts per county. Some are in more than 1 county. The list of registration districts can then be used to decide which Ellen Donnelly birth registrations on the civil registrations website Irish Genealogy.ie are worth looking at.
Registration District Map Browse function can also be used to find lists of civil parishes, towns and townlands within each registration district. Click on name of a registration district for list of civil parishes in the district. Click on name of a civil parish for list of towns and townlands in the registration district.
SWilson Info has many uses for Irish family history research, particularly for identifying places. It's another free site.
I believe that the website owner is a volunteer on an Irish FH forum, giving his time & expertise free, like RootsChat members do on this site.