You didn't leave your name so I apologise that I can't address you personally.
By 'specialisation' I'm guessing you mean a niche market. There are very many of these that life coaches can consider once certified. Examples might be relationship coaching, retirement coaching, coaching of young adults, career change coaching, health and wellness coaching and so on and so on.
The important thing is to complete a sufficiently comprehensive and broad based training programme like the New Insights Life Coach Training and Certification Programme. This will prepare you to be a high quality certified life coach. From there you can choose to focus on a specific niche or niches that are of specific interest to you.
As the principles, skills, tools and techniques are common, you will then simply need to adjust and adapt your coaching approach to meet the specific needs of your chosen niche. If you wish you can fine tune your knowledge of your chosen niche by taking short courses or reading further accordingly.