I couldn't get my son into school on a visitor visa unless I paid. This was in BC.
Even after I got my temporary work visa, I had to go through a rigid application including sending in my son's health reports and inoculation certificate. They also needed to see past school reports and a fixed lease showing my address, to prove my son was eligible for the school district. To be honest, it was easier getting my work visa than it was getting my son into school.
You could try applying for a student visa but again these are issued upon payment and acknowledgment from the school concerned.
Kindergarten school age children are exempt from this, by the way, any child over that age must have some sort of study visa.
Whether this applies in other Provinces, I have no idea.