I'm not sure what you mean by "in the system". What system? If the child is Canadian already, they can enter under their own merits as a Canadian.
The only place in the PR application form that a Canadian child would need to be listed, is in IMM5406 "Additional Family Info" form, Section B "Children". This is the same form you list parents and siblings.
I was under the impression that family members (including children) only listed on this 5406 form are not included on the COPR since they are not dependents, did not need medicals and so are not really part of the PR application. So even if you did update CIC office about your new Canadian child, I don't think COPR would need to be updated. Again i'm not 100% certain if Canadian children are listed on COPR, someone who has actually done this would need to confirm.