Is it permissible for a taxi driver to transport a person carrying alcohol in Canada, knowing that Canadian law penalizes the driver if he refuses to transport anyone?

If the situation is as you described, then you must seek lawful employment. If you do not find any and are compelled to take this job, then you should circumvent the law to avoid falling into the unlawful. This can be done by telling the person who asked you to deliver the alcoholic beverages that the car is not capable, and then busying yourself with repairing it or something similar. If you are unable to use stratagem and are forced to deliver it, then you must dispose of the payment in charitable ways, as you obtained it through an unlawful means.