OK, fresh eyes needed here to check my logic
I cannot see anything on births with father James Gibson and a mother McDougal(l) - I can however see a trail from Scotland for a couple, James Gibson and Mary MCLUGASH (this J.J. is the couple that you found in the 1881 Canadian census as a possible family for John).
There is a well researched tree also on Ancestry which has helped to confirm the likelihood on this possible family for John Gibson, with lots of sources that have been verified. J.J., with your experiece and knowledge of Canada, could you have a look at this tree (under parent search of James Gibson and Mary McLugash - owner roscr52)?
In essense, we have a James Gibson and Mary McLugash who married in 1852 Jan 21 in Kilchattan, Argyll, children showing to them in Scotland:
John - 30 Jan 1853 in Colonsay, Argyll...I think this is his baptim date from other sources
Margaret - 10 Sept 1854 in Colonsay, Argyll...this I think is birth date/ baptised early 1855.
Mary - 06 SEP 1856 in Jura, Argyll - shows on IGI and will show on the statutory records on SP
Christina - 4 Sept 1862, Ontario (she shows as aged 1 on the 1861 census in Canada, so not sure if the first Christina died and then next child also called Christina and born in 1862?)
The family show as arriving in New York, departing from Liverpool on the Ocean Monarch on 4 Aug 1860 - there is a shipping manifest entry as source for this.
There are also census entries for the family from 1861 to 1891 - including that 1881 census entry you found J.J. - in Bruce, Ontario.
There are a lot of additional notes on the tree regarding Mary McLugash and her family. I found this note interesting as it may explain the names McDougal and McLugash:
Rodrick's family [who looks to be a brother of Mary McLugash)
name on the Isle of Colonsay was McLugash (which is a sept of the McDougall clan). When Rodrick and his brother Hugh went to Dunoon on the Scottish mainland their surname was recorded as McDougall. Rodrick's widowed father Archibald McLugash, and three brothers John, Archibald and Donald McLugash along with their families went to Bruce County, Ontario, Canada where their surname was also recorded as McDougall.
This source gives a possible 1891 census entry for John Gibson in Assiniboia West, Territories (am I right in thinking this was in the Saskatchewan province which could then link with birth of first son James Arthur?):
John Gibson, 38, single, farmer, b. Scotland in Moose Jaw, Assiniboia West
There is a note on the family tree for this census entry which states:
John's cousins Archie and Donald McDougall were also thereThere is a lot more detail on the tree but just kept to the bare bones here!
Monica