Hello Rvche,
Since i did not reside in Canada when we submitted the sponsorship apllication, i did not cosign. And because i will be traveling to Canada with my son when he gets his PR visa then i didnt sign the declaration IMM5604. As proof of relationship, we submitted his birth certificate, passport, and in our country we have something called Family Judicial record its a paper identifying each member of the family (Father, mother, and children). But i dont think u have this in your country. So his birth certificate, and passport is enough if both the parents names are shown on them.
One more advise is to be prepared that it will take a long time for the application to be processed. My son was born in March 2019 and we submited the application on April 2019 ( just one month old baby) and last update was on June 2019. Since then we are waiting with no updates. Its surprising how long they take to process an application for a new born child with both parents already having a PR less than one year ago.