close to the possible year of birth you mentioned - there's a possible match, but you would be a good idea to start with the marriage to confirm the father's name for your Ellen, just in case this relates to a different Cunningham family :
Name: Ellen Cunningham
Registration district: Roscrea
Event type: Birth
Quarter and year: Jul-Sep 1905
Volume: 3 / Page : 450
Roscrea in BMD Index entries relates to the district which covered the town and a large area around it.
(there's a link to the note on ordering certs in the Introduction topic)
S.