Tonyrefail is registered in Pontypridd, (sub district Llantrisaint)
A birth shows up in the right quarter
Dec 1911 / district Pontypridd /vol 11a /page 1190
Mary J Morris - mother's maiden name Davies
The birth certificate would show the exact date, and the names of the parents.
I don't know if it is your Mary J, without something (just a little more) to go on.
But it is the only Mary J Morris showing up anywhere for the year and quarter.
If you got this birth certificate (from here
http://www.gro.gov.uk/gro/content/certificates/ ) and it has the right day/date of birth, you would have the parents' names, and the mother's maiden name.