What if, following the French and Indian War, Britain had traded the frozen tundra of Canada for the sugar islands of the Caribbean? Then, once Napoleon rolls along, French Canada, with its tiny population, could be taken by America.
Or Perhaps the Quasi-War becomes a true war and Alexander Hamilton takes Canada in the 1800s.
Under the circumstances, the Quasi-War almost definately becomes The Franco-American War and yes, Canada falls.
Even if the United States were successful in its aims during the War of 1812, I doubt its occupation of Canada would be anything more than a temporary affair. Outside a vocal minority, the idea was rather unpopular as Canadians were perceived as unable and otherwise unwilling to embrace the Republican values of the United States.
In Lower Canada, New Brunswick, Nova Scotia, definately. Those territories would be little more than a barganing chip as the cultures there probably were unwilling to embrace Republican values.
Upper Canada in 1812, on the other hand, had about as many residents who identified themselves as Americans as not, so Upper Canada could actually be a viable concession. Also, the Americans could demand that Britain cede it's claim to the Oregon (which if we're talking about modern Canada includes British Columbia) which is iffy.
Burning York wasn't exactly the best way to endear themselves to the locals, so I'd say it would require better conduct on the part of American troops in Upper Canada to make it viable. That and better leadership that could have won at Lundy's Lane, Queenston Heights, etc...
But if they pulled it off...
...Could they possibly purchase Ruppert's Land from the Hudson Bay Company?
If they could do that, eventually Britain would cede it's claim to the Oregon. British North America would be seperated from the Oregon by an expanse of land that's basically the whole of Ontario, Manitoba, Saskatchawan and Alberta. What's the point of maintaining the claim under those circumstances?
Hence, the initial intent of planners in Washington was that Canada was to be used as a bargaining chip at the negotiating table in return for Britain agreeing to end its harassment of American shipping (which essentially became a moot point with the repeal of the Orders in Council and the end of the Napoleonic Wars). So unless a very radical portion of the Western lobby succeeds in swaying the opinions of Congress and Britain is otherwise unable to take her possessions back by force, 1812 is probably out of the cards.
Exactly.
I would say, therefore, that America's best chance in taking Canada lie during the Revolution and even then it's a long shot.
A change of tactics a little better planning and an alternate route into Canada by the Arnold Expedition and the odds become shorter actually. Iffy, but not as improbable as some think.
Other possibilities include either the Caroline Affair or the Aroostook War escalating into some kind of wider conflict or presumably in the aftermath of a showdown following the Trent Affair.
Another possibility is "54/40 or Fight!" actually results in a full blown war over the Oregon, but those also present an opening for Manifest Destiny to head north.