The step mom can adopt the kid through CARA guidelines after 2 years of your stable marriage the procedure under CARA and legal formalities are given in below link

http://cara.nic.in/Parents/Eg_step_parents.html

If she is married to you. You don't require to do such adoption procedure. Still if you require you need to execute adoption deed and Approach court for the same

Your ex wife should agree to give the child in adoption to you and your second wife 

2) there should be giving and taking ceremony 

3) deed of adoption should be duly stamped and registered 

The Prospective Adoptive Parents (PAPs) should produce following original documents along with two copies on which self attestation is done for undergoing a legal adoption procedure.
1) Any of the following documents as Identity Proof – Pan Card/Passport/Voter Card/Driving License.
2) Address Proof - for example, any of the documents like Ration Card/Aadhar Card/ Electricity Bill etc.
3) Certificate of Marriage
4) The Prospective Adoptive Parents should obtain a Health Certificate from a registered medical practitioner stating that they are not coping with any incurable or contagious diseases or any mental or physical condition due to which they would prove incompetent to take care of the adopted child.
5) A Family Photograph.
6) Recently clicked Photographs of the Adoptive Family (three photographs of postcard size).
7) The self-employed Prospective Adoptive Parents need to furnish an IT Statement for the preceding three years. They have to provide an Income Certificate in case if they are employed in any organisation from that particular organisation along with the date of superannuation.
8) Two Letters of Recommendation are required to be furnished by Prospective Adoptive Parents. These letters of recommendation should be from the persons who are well acquainted with adoptive family and who are not the immediate relatives of any of the any of the Prospective Adoptive Parents.
9) Prospective Adoptive Parents also need submit Financial Statement which should include bank statements for preceding six months, particulars of loans taken and complete details of the moveable and immovable properties owned by them.
10) In case of previous adoption the Prospective Adoptive Parents have to furnish Adoption Decree.
11) If Prospective Adoptive Parents already have a biological or adopted children or child whose age is more than 7 years, they need to take Written Consent from such children or child.
12) Single Prospective Adoptive parents need to provide a Letter From a Close Relative stating that the relative would take care of child in case if any unforeseen circumstances take place.
13) In case of Divorcees (Single Prospective Adoptive Parent), Divorce or Legal Separation Decree needs to be submitted.

Dear Sir,

"Indian citizens who are Hindus, Jains, Sikhs, or Buddhists are allowed to formally adopt a child. The adoption is under the Hindu Adoption and Maintenance Act of 1956. Under this act, a single parent or married couple are not permitted to adopt more than one child of the same sex. Foreign citizens, NRIs, and those Indian nationals who are Muslims, Parsis, Christians or Jews are subject to the Guardian and Wards Act of 1890. Under this act, the adoptive parent is only the guardian of the child until she reaches 18 years of age. 
The Prospective Adoptive Parents (PAPs) should produce following original documents along with two copies on which self attestation is done for undergoing a legal adoption procedure.
1) Any of the following documents as Identity Proof – Pan Card/Passport/Voter Card/Driving License.
2) Address Proof - for example, any of the documents like Ration Card/Aadhar Card/ Electricity Bill etc.
3) Certificate of Marriage
4) The Prospective Adoptive Parents should obtain a Health Certificate from a registered medical practitioner stating that they are not coping with any incurable or contagious diseases or any mental or physical condition due to which they would prove incompetent to take care of the adopted child.
5) A Family Photograph.
6) Recently clicked Photographs of the Adoptive Family (three photographs of postcard size).
7) The self-employed Prospective Adoptive Parents need to furnish an IT Statement for the preceding three years. They have to provide an Income Certificate in case if they are employed in any organisation from that particular organisation along with the date of superannuation.
8) Two Letters of Recommendation are required to be furnished by Prospective Adoptive Parents. These letters of recommendation should be from the persons who are well acquainted with adoptive family and who are not the immediate relatives of any of the any of the Prospective Adoptive Parents.
9) Prospective Adoptive Parents also need submit Financial Statement which should include bank statements for preceding six months, particulars of loans taken and complete details of the moveable and immovable properties owned by them.
10) In case of previous adoption the Prospective Adoptive Parents have to furnish Adoption Decree.
11) If Prospective Adoptive Parents already have a biological or adopted children or child whose age is more than 7 years, they need to take Written Consent from such children or child.
12) Single Prospective Adoptive parents need to provide a Letter From a Close Relative stating that the relative would take care of child in case if any unforeseen circumstances take place.
13) In case of Divorcees (Single Prospective Adoptive Parent), Divorce or Legal Separation Decree needs to be submitted."

Dear Querist

adoption Deed can be registered as per Hindu Adoption and maintenance Act and your would be wife may take your son on adoption after your marriage with her. your ex wife's No objection and personal presence at the time of registration of adoption deed is mandatory and without her consent and appearance the registration is not possible.

Feel Free to Call

This is a case of adoption by step-parent.

You and the step mother here, need to register with Child Adoption Resource Information and Guidance System with the required documents as mentioned in Schedule VI.

To know the complete step by step process, pls visit: http://cara.nic.in/Parents/Eg_step_parents.html

You cannot change biological mother name of your son, with the consent of both biological parents your second wife can legally adopt your son as per Central Adoption Resource Authority(CARA) 

Dear Client,

Wife has renounced child right in court order. So now she can adopt him. Approach CARA, surrender the child than both of you adopt him jointly.

1. As per the information mentioned in the present query, makes it clear that as per the court order of divorce, or custody ( I am stating custody as this is not clear in the query as to whether you gone for custody or not) that you would be having the responsibility to take care of the child and your ex wife had refused to keep him with her.
2. After this detailed order, she doesn’t have any right on your child.
3. And yes, your now wife will have to adopt her legally by filing an application before the family court of your district along with all the valid court orders and your marriage proof etc. to become his mother legally.

As of now there is no provision in law for the step mother to adopt the child of her husband's first marriage.

Thus she can remain as a step mother only