Family records indicate that James was born about 1840 , would it be possible to see if there is a birth record for him with a father William Taylor.
Civil registration of births started in 1864- before this date there are no birth certificates.
It would appear that checking the Church Register at the Agadhowey presbyterian church might provide some more information on Jame's family and his father William.
Again, the information you are looking for does not exist. Aghadowey Presbyterian baptisms start 1855, marriages from the start of civil registration in 1845 and, like most Presbyterian churches, there are no death records.
There is a marriage of a Taylor girl in 1840s with father William which I'll post later but no way to know if she belongs to the same family (and if she does, how she would be connected).
Added- 20 Oct.1848 William Duff, bleacher, Carnrallagh, son of David Duff, farmer, to Sarah Jane Taylor, Mullahinch, daughter of William Taylor, labourer.
No Taylors listed in the following records for Aghadowey Presbyterian Church-
1850-Nov.1854 Pew List
1852-1853? Names of Subscribers for paying off a debt of borrowed money expended in building Aghadowey Meetinghouse
1 Jan.1863 Names of those who have paid their assessment
