The 1894 marriage register entry gives you the parents as:
Robert BARNES and Mary Jane BARNES, previously McFARLANE, MS OLIVER
and
Robert IRWINE and Elizabeth IRWINE MS ARCHER
First try a short cut and look for marriages of these couples. There's one
Search also for the death register entries of the parents found on the 1894 marriage register entry. You should quickly locate those for Robert and Elizabeth, but, again, wildcards are required, - IR?IN* ......
Robert and Mary appear in the 1881 census at
Dwelling: West Bridgend Black Bull Buildings
Census Place: Cardross, Dumbarton, Scotland
Source: FHL Film 0203549 GRO Ref Volume 496 EnumDist 15 Page 11
Marr Age Sex Birthplace
Robert BARNES M 35 M Ireland
Rel: Head
Occ: Furnaceman In Forge
Mary BARNES M 45 F Ireland
Rel: Wife
Thomas MC FARLANE U 21 M Dumbarton, Dunbarton, Scotland
Rel: Stepson
Occ: Ship Fitter
David BARNES 12 M Dumbarton, Dunbarton, Scotland
Rel: Son
Occ: Scholar
William BARNES 11 M Dumbarton, Dunbarton, Scotland
Rel: Son
Occ: Scholar
Robert BARNES 8 M Dumbarton, Dunbarton, Scotland
Rel: Son
Occ: Scholar
William ROBERTSON U 27 M Dumbarton, Dunbarton, Scotland
Rel: Lodger
Occ: Rivetter In Shipyard
They also appear in the 1871 census, probably the same address.
So, with the other census record in a previous post, you know that all the parents shown on the 1894 marriage register entry were born in Ireland.
To tie the various records together, and get absolute proof, you will need to look at a couple at least of the birth register entries of kids who show up in the various census entries.
David