Nothing short of consultation with a local experienced and very adept family practitioner will meet your sister's needs, and is not likely to be available at no charge. Her mental competence at the time of the adoption may be relevant. Be aware that adoptions as a general rule are irrevocable, but if the partners are splitting custody of the child may need to be determined in court proceedings.
Best wishes for an outcome you can accept and please remember to designate a best answer.
This answer is offered as a public service for general information only and may not be relied upon as legal advice.
I agree with the previous post. Your sister will need to speak with an experienced family law and adoption attorney. Her mental health will need to be discussed with the attorney. Simply because she has mental health issues does not necessarily mean that she is incompetent for the purposes of entering and agreeing to legal contracts.