Hi,
As Gortonboy writes, I think the marriage certificate would be a good place to start as it should give you John's father's name (possibly Martin) and occupation, and also may indicate whether or not his father was alive at the time of marriage.
Marriage Index from FreeBMD:-
Marriage of John Brophy and Mary Lonergan
Year: 1886
Quarter: 2/June
Registration District: Bolton
Volume: 8c
Page: 476
In case you haven't ordered certificates before, here is the link:-
https://www.gov.uk/order-copy-birth-death-marriage-certificateAs Civil Registration in Ireland only began in 1864, you may not be able to get a birth certificate, however, if you can confirm John's father's name, you may be able to find a baptismal record in one of the parishes in Co. Kilkenny.
Best of luck!