Dear Mary:
Is this the family:
http://www.census.nationalarchives.ie/pages/1901/Kilkenny/Knocktopher/Barrettstown/1454664/
If so, you can view the civil birth records for the children who are listed on the Census form and work backwards.
I also have a copy of the civil marriage record which I attach and which you refer to. You will note that Ellen Dwyer was a witness to Mary's wedding. This may be a sibling of Mary's.
There is a civil death record for a Patrick Dwyer who died in 1884. His daughter, Ellen Dwyer was the person who registered his address. You will note that his residence is given as Baysrath. He is listed as 82 years of age and a widower. Was this Mary's father? If so, it might be worth looking for a death record for a Mary Dwyer before 1884.
Looking at the occupants or households of the 1901 Census in Barrettstown, I note that there is a Richard Dwyer who resides there in House No. 3. This family may be a connection to Mary Dwyer due to their proximity (James Dalton is House No. 1).
When I searched for a baptism record for Richard Dwyer, there is one for a Richard Dwyer baptised on 10 February 1846. His residence is Baysrath and his parents are Patrick Dwyer and Mary Lahy. (Attached).
Baysrath townland borders Barretstown and it may be that the name was used interchangeably if this family lived very close to Barretstown. https://www.townlands.ie/kilkenny/kells/dunnamaggan/baysrath/
Alternatively, you can see if the local church has a burial register. Often, these registers would list where the deceased is buried. The contact details for Ballyhale parish office are here: http://knockcar@indigo.ie
It was not uncommon for families not to have headstones as they were expensive, and if many family members had left, there was often no one left to purchase one.
If you need any further help, please let us know.
Please let us know when you are planning on travelling.
All the best,
Jane