In Ontario, there was recently the Parent A, B, C case in which a lesbian couple and a known donor/male coparent or somewhere in between, were all listed as parents.
I don't know if you're interested in that option.
EGALE would know. I doubt you'll find anyone from Manitoba on here, and birth certificates are a provincial issue.
The legal advice I was getting in Ontario (though 3 years or so ago) was to go through with the second parent adoption *anyway* because if something happens outside Canada, especially in a US DOMA state, or possibly in another province, you may have a problem.