British North America until 1867, Canada after confederation
So you're really asking if the UK and the US were likely to have gone to war again after the 1812-15 conflict.
Historically, there were several, all of which were ended peacefully because both the US and the UK had too much at stake economically in peaceful relations; however, these were the closest:
1) Aroostook Valley Conflict, 1838-39
2) San Juan Islands Conflict, 1859
3) US Civil War, generally; Trent Affair (1861), Laird rams (1863) are probably the two closest appoaches to actual causus belli;
4) Fenian Raids (1866-71) of which the 1866 raids (Ridgway) were the most likely to lead to a real conflict.
More AH, but at least in the realm of the possible, would be something in 1837-38 connected with the rebellions in Upper and Lower Canada (Mackenzie and Papineau and the Hunters Lodges, i.e. Patriots' War).
Best,