If you are white, particularly a white male, you are likely SOL. Section 15 of the charter of rights and freedoms is as written:

15. (1) Every individual is equal before and under the law and has the right to the equal protection and equal benefit of the law without discrimination and, in particular, without discrimination based on race, national or ethnic origin, colour, religion, sex, age or mental or physical disability. (2) Subsection (1) does not preclude any law, program or activity that has as its object the amelioration of conditions of disadvantaged individuals or groups including those that are disadvantaged because of race, national or ethnic origin, colour, religion, sex, age or mental or physical disability.

White people (and white males specifically) are generally considered not to be "disadvantaged individuals" and as such, companies are to some degree allowed to discriminate against non-disadvantaged individuals in pursuit of "equality". Given how awful our courts are, I would not expect any judge to side favorably on this issue. You might have a shot if you fall under any other racial category.

That said, if you only have to "self-identify" as black, who are they to say otherwise? They can't ask for medical data proving anything, and there is no status card for black people like there is for aboriginals.