These dates are probably too early for most records in Ireland.
Found nothing for Armag in either Antrim or Armagh
Gilford, Down Gilford was a town in Co. Down in a Parish
Tullylish which was either in the Union of Banbridge or
Fletcher's in the Griffith Valuation in 1864 show up in
Shankill, Armagh in the Union of Lurgan and in the Parish of Seagoe in the Union of Lurgan.
A poor law Union and later civil registration district would cover an area of 12 miles from the town, if close to a border can cover 2 counties or even three in some cases but no more than the 12 mi. Counties Armagh and Down share a border with each other Down on the east coast and Armagh to the west.
Lurgan has RC baptism records from 1822; Seagoe from 1836 and only two Church of Ireland Parish's have baptism records
Parish Armagh from 1801-1822 and marriages from 1801-1822 and 1845-1921.
Irish Wills Index 1536-1858:
John Morton, Dogher Parish Shankill, Armagh Probate 1733
You should try the Registry of Deeds - google and look for rootsweb.