Under NAFTA, American and Canadian instructors are free to instruct in each country, without having a greencard/social insurance card. All you need to do is find a flight school to sponsor you.
Keep in mind, however, that instructing is very different in Canada. There is no such thing as a CFI, CFII, MEI, etc. We use Classes.... a class 4 is your beginner. To get to higher classes you need certain requirements (ie. solo recommends, passes, etc). It's also very unlikely that a new class 4 would get to do some multi teaching here.
Anyway, good luck.