Hmmmmm ... I've been through the candidates at ellisislandrecords.org -- difficult to narrow down.Very few Mary Tierneys ...
Did they baptize the children catholic?Maybe their certs would show a Foley sibling as a godparent, and thus another paper trail?
Foley/Tierney ... ?Was Mike Joy her 2nd marriage and widowed by a Foley?Or, maybe born a Tierney and raised by a Foley, or vice versa?Looking at the 2 birth certs, interesting."Mary E. Tierney" on Nora's.
In theory, she should be on the 1901 census ...when you have a few more clues, this might be helpful.