Hi, I looked about for births for Bernard Riley/O'Riley in Galway and could not find any specifically in co Galway but found several in adjoining counties which could possibly be him. The ones that I have found, have also, in at least half the cases, been registered in a 2nd county.The ones I found were mainly listed under Reilly as opposed to Riley which is a variation on the name that you should consider.
Births for Bernard Reilly/Reily:
bap: 11 May 1788
Delvin, co Westmeath
parents: James Reilly & Mary Keogan
bap: 25 May 1792
Granard, co Longford
parents: Terence Reilly & Mary Reilly
bap: 11 Aug 1796
Delvin, co Westmeath
parents: Luke Reilly & Margaret Hays
bap: 10 March 1783
Granard, co Longford
Luke Reilly & Margaret Reilly
* this is probably the 1st son & the above is 2nd one they named Bernard
bap:6 Oct 1782
Granard, Longford
parents: Bernard Reilly & Mary Reilly
bap: 17 June 1798
Clonmellon, co Westmeath
parents: Michael Reilly & Rose Crosby
bap: 4 Nov 1781
Granard, co Longford
parents: Phillip Reilly & Rose Donoghue
bap: 11 May 1788
Milltown, co Westmeath
parents: Michael Reilly & Elizabeth
bap: 13 Nov 1795
Granard, co Longford
parents: Laurence Reilly & Esther
bap: 18 Sept 1796
Granard, co Longford
parents: James Reilly & Mary Mulligan
If I might make a suggestion. You really need to spend a few bob and get copies of the death certificates for both Bernard Riley & his wife Mary to see if they have any helpful info on them. Even one parents name would narrow things down. Also, you need to get a copy of a birth or baptism for the children or just a couple to see if any other family may be listed, perhaps as sponsors. Sometimes if you can find a brother or sister to the person you seek, you can trace them to find your relation. But the death certs would help pinpoint which one of the Bernards baptisms is for your fellow if any at all are. Hope this helps, Kim