Margaret
You haven't explained why you are looking in Dublin in the first place - the 1901 Census simply says Dunnock More, Ireland.
If you look at the 1891 Census of England, you will find mention of Patrick Morris, coal miner, b Co Tyrone c1866 [insignificant difference], living in Tow Law, Hedleyhope, Co Durham.
It looks like you should probably focus on Donaghmore, Co Tyrone.
Adrian