I think the key to taking Canada would probably require a similar chain of events leading to the UK losing the US: an overwhelming coalition that the Brits couldn't possibly defeat, leading to them having to make 'tough choices' as to which colonies they preserve. Canada is never going to achieve independence on its own, and neither will the US conquer it without any outside help.
1. 1836. Rebellion in Upper Canada is imminent. London bows completely to the ultraconservatives, instituting harsh and repressive measures against the Canadians that squash rebellion for the time being, but generate intense long-term resentment of British rule. Such repressive measures include stopping immigration from the UK/Canada to the USA.
2. Great Irish Famine. Irish people emigrate en masse away from Europe. Owing to the ban on immigration to the US, the top destination for Irishmen becomes Canada. Upper and Lower Canada become populated by people who have long-term grievances against the British.
3. 1st Anglo-Sikh War. Civil War breaks out in the Sikh Empire after the death of Ranjit Singh in 1839. The East India Company sees an opportunity, and war breaks out in 1840 (5 years before OTL). With 5 less years of internecine bloodshed for the Sikhs, they manage to hold out for some time against the British, collapsing in 1844. This war shows to the Indian rulers and sepoys that the British armies are not invincible. Additionally, the failure to end the Sikh War promptly costs Lord Hardinge his post as Governor-General of India and Dalhousie takes his place in 1842 (6 years before OTL).
4. Dalhousie immediately puts into action his "Doctrine of Lapse", annexing aggressively Indian principalities with no legitimate male heirs. Indian princes now begin to question whether it is worth living under British protection. Resentment among the Indian elite builds up for a few more years longer than OTL.
5. Great Indian Mutiny (perhaps a few years earlier than OTL). Indian troops revolt in force across India (and not just the Gangetic plain as in OTL). Princely kingdoms rise up against their colonial masters. British rule collapses entirely and is confined to a few areas around Bombay, Calcutta and Madras.
6. Desperate to protect its 'jewel in the crown', British forces are withdrawn from all corners of the globe in order to crush the rebellion, Canada being one of them. Irish nationalists take the chance to revolt across Canada, some openly discussing Union with the USA.
7. The world watches the British Empire totter. Russia sees a unique chance to destroy the power blocking it from attaining a port on the Indian Ocean. France under newly-crowned Emperor Napoleon III sees a chance to bolster his regime, as well as to avenge his uncle. The US, fresh from their trouncing of Mexico, begins to call for war once again, southerners reasoning that the incorporation of Canada will give them reason to throw off the Compromise of 1850.
8. USA declares war on the UK. American troops march into Canada and occupy it with little resistance. The UK institutes a blockade of the US but can do very little on land, its armies still fully concentrated on subduing India.
9. Russia and France call a conference to deal with India, much to the UK's chagrin. The British Empire can ill afford another war with two European powers, however, and so it agrees to negotiate.
10. France is worried that the end of British power in India will lead to a massive surge in Russian power as it finally obtains its warm-water port. It is also keenly aware that Russia will be a future enemy, as it is now making demands on the Ottoman Empire regarding Orthodox Christians (the Crimean War doesn't happen in the 1850s OTL).
11. Conference of Paris. In return for a 'free hand' in India, the UK concedes spheres of influences in Persia and Central Asia, also ceding Canada to the USA. Secretly, in return for recognizing its Canadian gains (and also a guarantee of neutrality in the upcoming war for Cuba, as Southerners are now demanding after their 2 victories), the US gives its tacit approval for France to intervene in Mexico.
BTW, this scenario is probably not Americawank. Despite controlling Canada in addition to the Southwest, the USA is now in the thrall of jingoistic Southerners demanding constant expansion in line with so-called 'Manifest Destiny'. Eventually they will either collide with entrenched European interests, or rip themselves apart in an even bloodier Civil War.