I search Irishgenealogy.ie, a new, FREE, online database of surviving Co. Kerry church B/M/D records. There are more than 14,000 B rcds containing the name Mary Connor(s) somewhere on the record in this database.
For Patrick Murphy, the number is 3,352.
Suggest you find some reasonably accurate DOBs/POB, parent(s) name(s), and/or placename(s) to refine your search using this database. Your great aunt Kathryn's notes on the trip should contain some of this info.