Your uncle or cousin can not sponsor you to Canada under the federal system, only if they live in a province that has a family class under their provincial nominee program. There are other requirements too. I am guessing it would take a minimum 6 months to get the PR visa. Maybe closer to one year. After getting the visa, you would have to come to Canada and "land" and you would get your PR card a month to 6 weeks later. After getting a PR card, you have to live in Canada at least 730 days out of every 5 years to keep it.
Check into the provincial nominee program of the province where they live. You can find all of them at
http://www.cic.gc.ca/english/immigrate/provincial/apply-who.asp