There is no central registry of births and deaths in Canada. Canadian birth and death certificates must be obtained from the vital statistics office of the province in which the event occurred. They cannot be obtained through the Canadian Embassy. Requests should be sent directly to the appropriate provincial vital statistics office. The fee for issuing birth or death certificates will vary from province to province.
You cannot obtain a Canadian birth certificate for a Canadian child born outside of Canada. You must apply instead for a Canadian citizenship certificate.