Hello,
Rootschat is not set up for finding living people - but I think we can give you some information and suggestions that might help.
Canadian privacy laws are very strict. Birth registrations from the 1950s will not be in the public domain - whichever Province this lady was born in (Registrations fall under Provincial rather than national, jurisdiction). I have included a link to the "Civil Registration" guide from the Vancouver Public Library. It is a very good description of what records are available in each Province (scroll down and you can see the tabs).
http://guides.vpl.ca/genealogy/civilregistrationIf you have an idea where in Canada this lady was born or where she might be living now, that would be very helpful!! You can check voters' lists (available on Ancestry... your library might have access to the free Ancestry Library Edition), you can look at local newspapers for things like a marriage announcement, the birth of her children, perhaps she might be mentioned in the obituary of a relative (her mother/grandparents etc). There is also the Canada411 site ... it is an online phone book. You might also try looking for her on social media - especially if she is trying to find her family too.
These are just a few ideas. I hope other people can add to the list.
Good luck
RK