Thanks to all for your help on this, while looking for my Clarke family, I found came across some more Clarke's who were shoe/boot makers. I am not sure if they are connected to my Charles Clarke of Barrack Hill, Armagh (b c 1846) or not. I think I also found the death for Charles father Peter, who died on 23/11/1886 at Callan Street. Informant was Charles Clarke.
For the benefit of anyone else researching Clarke family in Armagh, these others were:
John Clarke b c 1866 in Callan Street, Armagh, a Shoemaker. married a Margaret Jane McBride. His father was George Clarke, a Shoemaker, b c 1846. Could George be a brother to my Charles I wonder? John and Margaret had at least 12 children. They lived in Callan Street, then Cathedral Close and finally Dawson Street.
George (Georgii) Clarke, a Shoemaker, b c 1832 who married an Ann Lennon. Could George be a brother to Charles Father Peter? They had at least 4 children, all born in Callan Street, Armagh.
William Clarke, a shoemaker, b c 1838 married an Elizabeth McCardle. Had a daughter in 1865 at Callan Street, Armagh. Is William another sibling of Peter Clarke, father of my Charles?
I hope this helps someone and thank you everyone for your help.