DEED OF ADOPTION

For the general format of  "Deed of Adoption" kindly go through the attached document

As you are saying that your cousin is planing to adopt a baby girl from his "Relative", so just prepare the "Deed of Adoption" and get it Registered before the Concerned District Sub Registrar of your District and State.

For further details, procedure and legalisation kindly go through the following website:

https://www.adoptionindia.nic.in/

you should go through some adoption agencies to adopt a baby. The benefits of that are : 1. you need not to go anywhere to prepare adoption documents, 2. you will get better legal advice there, 3. you will get all the necessary information from A to Z under one roof... 

It is always better to take help of the professional in the field - You may adopt with good intentions but later due to technically faulty or otherwise defects in the documents the sufferer could be the one getting adopted. 

Legal understanding by non-professionals by reading on their own may sometimes cause problems -

Sardarji got the fourth child.He fills data in the birth certificate.
“Mother: Sikh.Father: Sikh.Kid: Chinese.”

“How come you write “Chinese” when both parents are Sikh?”
” Aah, read a newspaper, it says that every 4th person born on the Earth now is a Chinese.”

Legal interpretations by non-professionals could be like the sardarji -

Agree with Adv. Gundlapallis