Tradition was to marry in the bride’s church so Brigh Presbyterian may be the place to look for her baptism, and that of any siblings. I note that Mary lived in Annaghone and that one of the witnesses at the 1858 marriage was a William McWhirter. I wonder if this is him in 1901:
http://www.census.nationalarchives.ie/pages/1901/Tyrone/Tullaghoge/Annaghone/1730073/
1911 census:
http://www.census.nationalarchives.ie/pages/1911/Tyrone/Tullaghoge/Annaghone/859763/
I note that in 1859 Griffiths Valuation has a Jane McWhurte(r) in a weaver’s house (plot 5b) on John Henderson’s farm in Annaghone. Her name remains as tenant until 1888 when she is replaced by William (suggesting she died around that time). His name remains there until 1921 at which time the property is noted as being dilapidated but still with a good roof.
Possible death for Wm McWhirter registered in Cookstown 3.5.1918. The age (56) doesn’t reconcile with the census information but ages were sometimes wildly inaccurate on death certs. Or there might be a transcription error.
Brigh Presbyterian records have been copied and are held in PRONI in Belfast. A personal visit is required to access them.
If Jane McWhurte(r) was Joseph’s wife, the Griffiths information suggests he had died by 1859.