It really depends on which province you happen to be in. There are some providers, extra-jurisdictional or providers from outside of Canada, that will accept a production order from Canada. That being said, depending on the province you're in, a justice or a judge may not actually sign your production order, because they do not believe they have the jurisdiction to order a company outside of Canada to action whatever the order is.
Short of that, the alternative would be the mutual legal assistance process. It takes a considerable amount of time and resources to actually get that completed. Then you're looking at maybe six months, a year or something like that for the response time, depending.