As a PR, you must be resident in Canada to sponsor your child. There is some splitting of hairs concerning if you are still resident in Canada even if you are on a short leave in India but if immigration finds out that you are trying to sponsor your child and you are not in Canada at the time, they may well deny your application. In order to be in Canada and sponsor your child, you can either go to Canada yourself and leave the mother with the child in India or you can apply for a TRV for the baby to come with you. If the TRV is denied based on that the baby will be staying in Canada permanently, then you can apply for a TRP.
Being due for Canadian citizenship is irrelevant. If you become a citizen before your baby is born, your baby will automatically get citizenship. If not, then you are still a PR and need to sponsor your baby for PR.