I'm editing this to note that Roger (see next message) found a likelier townland named Dowras (given that it is near Birr). I'll still leave my info here, in case any of it proves helpful.
There is a townland called Dowra in County Cavan, and you can see more info about it at this link: https://www.townlands.ie/cavan/tullyhaw/killinagh/dowra/dowra/
The Birr you mentioned is probably the town of Birr in County Offaly (where some of my ancestors lived). It was customary to station policemen somehwere other than where they grew up, to avoid favoritism, and perhaps he met Martha there. Weddings usually took place in the bride's parish
Dowra is in the parish if Killenagh, and the online parish records there go back to 1869, so you might be able to find something there, at this link: https://www.townlands.ie/cavan/tullyhaw/killinagh/dowra/dowra/
The online parish records for Birr go back to 1838, so you may be able to find their marriage record, and perhaps info about Martha's baptism and family members there (if it was in fact her home parish), at this link: https://registers.nli.ie/parishes/0763