The registration of birth must be done at the Embassy within one year of the Child's birth. When birth of a child is registered with the Embassy or Consulate within one year from the date of birth, the child is automaticallyeligible for 'Citizen of Indiaby Descent' under Section 4(1) of Indian Citizenship Act, 1955.

2)the application is made within one year of birth of child as per above-mentioned process and subject to fulfilment of the eligibility criteria according toMinistry of Home Affairs guidelines, the Embassy of India shall register the birth of the child as an Indian citizen and issue the Birth Registration Certificate. Where application is made after one year of birth of the child, the process is the same except that such application will be forwarded to Ministry of Home Affairs for approval.

You can do it if you have a document to support the same with you for place of birth 

Citizen of India by descent: You are Citizen of India by descent if you are born outside India and either of your parents is a citizen of India at the time of your birth.

A:Indian passport can be issued to the "Citizen of India by Descent" i.e. person born to Indian parent(s) outside India. First parents need to register the birth of Child in Consulate.

It is mandatory to apply for Indian passport of the Child alongwith registration of birth. The registration of birth must be done at the Indian Consulate within one year of Child's birth.

please submit a copy of the proof of place of birth, along with the originals for verification.

If the embassy had sought approval from MHA in  India, then you may have to wait

Since you have complied with all the requirements as per procedures of law with the Indian embassy, it becomes the duty of the Embassy to send the papers to MHA, New Delhi and get their approval.

So you may wait for the decision.

Embassy forwards your application to MHA 

Dear Client,

Contact the Ministry of Home Affairs (MHA): If the Nigerian Indian Embassy requires instructions or approvals from the MHA in India, you might need to initiate contact with the MHA. You can reach out to the MHA through their official channels and explain your situation. They might be able to provide guidance on the necessary steps and approvals required.

Document Gathering: Make sure you have all necessary documents related to your wife's birth, including the birth certificate from the hospital in Nigeria, the birth attestation from the National Population Commission of Nigeria.