Under Immigration Rules Part 8, paragraph 319J, both parents need to be settled before you can apply for settlement for the child . They can wait (assuming the child will not leave the UK) until the mother is also settled and then they can apply for the child's ILR.
319J. Requirements for indefinite leave to remain
To qualify for indefinite leave to remain under this route, an applicant must meet the requirements listed below. If the applicant meets these requirements, indefinite leave to remain will be granted. If the applicant does not meet these requirements, the application will be refused.
Requirements:
(a) The applicant must not fall for refusal under the general grounds for refusal, and must not be an illegal entrant.
(b) The applicant must be the child of a parent who has, or is at the same time being granted, indefinite leave to remain as:
(i) a Relevant Points Based System Migrant, or
(ii) the partner of a Relevant Points Based System Migrant.
(c) The applicant must have, or have last been granted, leave as the child of or have been born in the United Kingdom to, the Points Based System Migrant, or the partner of a Points Based System migrant who is being granted indefinite leave to remain.
(d) The applicant must not be married or in a civil partnership, must not have formed an independent family unit, and must not be leading an independent life, and if he is over the age of 16 on the date the application is made, he must provide the specified documents and information in paragraph 319H-SD to show that this requirement is met.
(e) Both of an applicant’s parents must either be lawfully settled in the UK, or being granted indefinite leave to remain at the same time as the applicant, unless:
(i) The Points Based System Migrant is the applicant’s sole surviving parent, or
(ii) The Points Based System Migrant parent has and has had sole responsibility for the applicant’s upbringing, or
(iii) there are serious and compelling family or other considerations which would make it desirable not to refuse the application and suitable arrangements have been made for the applicant’s care, or
(iv) One parent is, at the same time, being granted indefinite leave to remain as a Relevant Points Based System Migrant, the other parent is lawfully present in the UK or being granted leave at the same time as the applicant, and the applicant was granted leave as the child of a Relevant Points Based System Migrant under the Rules in place before 9 July 2012.
(f) The applicant has demonstrated sufficient knowledge of the English language and sufficient knowledge about life in the United Kingdom, in accordance with Appendix KoLL, unless he is under the age of 18 at the date on which the application is made.
(g) If the applicant is a child born in the UK to a Relevant Points Based System migrant and their partner, the applicant must provide a full UK birth certificate showing the names of both parents.
(h) All arrangements for the child’s care and accommodation in the UK must comply with relevant UK legislation and regulations.
(i) The applicant must not be in the UK in breach of immigration laws except that, where paragraph 39E of these Rules applies, any current period of overstaying will be disregarded.
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