The problem with any scenario that relies on tension between America and the UK is that, from quite early in the 20th century, Canada was transitioning into an independent and sovereign nation that was well aware of the impossibility of it defeating the US in any serious conflict. It's conceivable, if unlikely, that you could have a UK stupid and arrogant enough to commit blunder after blunder until America has been so thoroughly alienated that war between the two countries becomes a possibility. What's harder to imagine is Canada sitting idly by and letting the UK drag it into a war that it knows it will be the front-line of.
Any time after WW1, Canada is much more likely to throw up in frustration with the UK and aim for neutrality rather than getting involved in an unequal contest that it will certainly lose. That will cause some political and legal headaches if it happens before 1931, but we'd be looking at a world where the relations between the UK and US were very different to begin with, and any change at that scale is going to mean a different Canada almost by default. It should go without saying that after Canada obtains its legislative independence from the UK, no amount of tension between the UK and the US is going to automatically bring Canada into the war. Whether that occurs in 1931 or earlier or later, at that point the cause of the war would need to exist between Canada and the US specifically.
An alternate WW1 is a better bet, but the UK losing WW1 hard is more likely to lead to a nominally independent Canada that's fully within the American sphere of influence than it is to an invasion and annexation. Why waste blood and treasure and international ire taking Canada by force? A WW1 where the US is part of the Central Powers and invades Canada during that conflict is a more sensible option for an invasion, but getting the US into the Central Powers is going to be tricky without changing things between the UK and the US so much in the 1800s that Canada as we know it might never form.
"Peaceful" annexation options have their own merits and flaws when it comes to plausibility, but don't seem to fit the OP's request for an invasion along with the annexation. It's not an invasion when you're invited it.
Any time after WW1, Canada is much more likely to throw up in frustration with the UK and aim for neutrality rather than getting involved in an unequal contest that it will certainly lose. That will cause some political and legal headaches if it happens before 1931, but we'd be looking at a world where the relations between the UK and US were very different to begin with, and any change at that scale is going to mean a different Canada almost by default. It should go without saying that after Canada obtains its legislative independence from the UK, no amount of tension between the UK and the US is going to automatically bring Canada into the war. Whether that occurs in 1931 or earlier or later, at that point the cause of the war would need to exist between Canada and the US specifically.
An alternate WW1 is a better bet, but the UK losing WW1 hard is more likely to lead to a nominally independent Canada that's fully within the American sphere of influence than it is to an invasion and annexation. Why waste blood and treasure and international ire taking Canada by force? A WW1 where the US is part of the Central Powers and invades Canada during that conflict is a more sensible option for an invasion, but getting the US into the Central Powers is going to be tricky without changing things between the UK and the US so much in the 1800s that Canada as we know it might never form.
"Peaceful" annexation options have their own merits and flaws when it comes to plausibility, but don't seem to fit the OP's request for an invasion along with the annexation. It's not an invasion when you're invited it.