First of all a Canadian citizen can stay as a visitor (tourist) in the
UK for 6-months, subject of course to them providing the UK border entry agent (immigration control) the purpose of their visit (is a vacation), show that they have a return ticket, as well - in your case that you are staying with your friend (letter from him confirming this) & that you have access to sufficient funds to support yourself during your stay
As a visitor (entry visa stamped in your passport), you wont be able to work, or have access to any UK services or public funds while there as a visitor - simply visit & stay with your friend for the short duration & see if it's what you want in the relationship is doable - is my suggestion to you.
On the basis that the relationship is right for you (now or in the future) & you find its going to be long term, then the only immediate suggestion for you is to maybe apply for a fiance('e) visa & that your friend also agrees with this approach.
http://www.ukba.homeoffice.gov.uk/visas ... oposed-cp/If this is not what you want or is NOT possible in terms of the relationship, then there are very few choices left available to you.
The only other possibility without knowing your full details, which may not apply to you (or maybe it will) due to the time that you've known your friend (the two year rule) - is the unmarried partner visa, which requires you to prove a relationship has existed for at least two years.
http://www.ukba.homeoffice.gov.uk/visas ... you-apply/You have not mentioned if you (know about) qualify for an ancestry visa - whereby one of your parents or grandparents was born in the UK, or in one of the EU countries.
If thats the case, then you have further options available to you for an indefinite stay in the UK - subject of course to some conditions, such as accommodations, job, money etc
Good luck to you
Disclaimer: I am not an immigration expert & anything that I post on visa & immigration is based soley on more than 30 years of personal experience & interaction with the UKBA & Home office.