There are different types of therapy used with children. Play therapy, drama therapy, arts therapy, music therapy and probably more. However, most of those require a first degree and professional experience in the main discipline, then postgraduate training on top. Also, the employment prospects can be quite niche: I have worked in, visited and been associated with many schools and have only come across two schools that employed a play therapist.
On the other hand, there is also child psychotherapy, which would require a specific psychotherapy training.