REILLY-BUTLER from Cavan-Dublin to Salford

[Milliepede]

Yes the General Register Office now has a search for births and deaths where the births give mothers maiden name and the deaths give ages - very helpful.

The births go up to 1916.

There are deaths that could match up with the births.

Marion Reilly Dec 1906 Salford - age is given as 15 but is sometimes unclear with infants as it could be 15 weeks or 15 months

Gerald Reilly Dec 1914 Salford age 2

George I haven't found anywhere.

[aghadowey]

Another male child born 26 Dec 1900 at the Rotunda Hospital, is also great news. He was possibly named Luke, if we can assume the Irish naming tradition continues. Though, is there a reason for no name on the record?

All but one of those births don't list any names for the child. It's likely that the parents hadn't had time to think of names but the informant (likely staff member) just registered those births.
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1900/01976/1761350.pdf

[dathai]

Laurence Reilly born 1897 to Andrew a COAL PORTER and Rose Butler
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1897/02140/1812621.pdf

Andrew Reilly 1901 Jervis St Hospital age 32 born Westmeath,COAL PORTER, married
number 28 here
http://www.census.nationalarchives.ie/reels/nai003773115/

suggest you try workhouse records for wife and children as she would have had no income,hospital record says 2 months suffering with Pneumonia.