The rules from BLS and the CGI Toronto are ambiguous, so I am wary of you receiving incorrect advice from myself and/ or others here. I suggest you call BLS and ask them for advice and what best to do.
I can tell you that I am in a relatively similar situation. I lived in India from 1999 to 2009 and my residence there was in Bangalore in an apartment where no one I know currently lives. My Indian passport has showed that address since 2006. I do not have an adhaar card because of my limited time spent in India. My mother recently moved to India and lives with my uncle in a city I have never lived in. She owns property there but no one lives in that house. She had no adhaar card either.
BLS advised me to fill the PCC application with my mom’s property address, and suggested that my mom go to the police there and give them a heads up of the situation. My mom had to get an adhaar card, and I submitted that as address proof.
So I can see two possibilities for you:
1. If your parents reside in India, you can submit their address as your address in the PCC and submit their address proof (passport or adhaar card). Your passport proves they are you are parents (the name of your parents on your passport should match that of your parent’s address proof). The police would come to your parents house to verify and they are to tell them you are their son but don’t reside there.
2. I am not sure you can use the Bangalore address, since your parents do not live there. But you could check with BLS if it is ok if your cousin can go to the police station and give them a heads up of the situation. (BLS told me the address had to be my parents, and not any other relative, so I don’t know if this would work).
Again, call BLS and get advice from them. Some of their agents are terrible, but some are knowledgeable and helpful.