In japan, people get birth certificate from hospital after they were born. By submitting this paper to the city, he/she will be registered in the Koseki Tohon. The Koseki Tohon /Kaiseigen Koseki Tohon is/are equivalent to the so called 'birth certificate ' in other countries.
it should be okay for you.
In my case in 2014, I submitted the Koseki Tohon and Koseki shohon(it's just an extraction of the information from the Koseki Tohon ) for my son . It was okay.
This year, I submitted the Koseki Tohon and shohon for sponsoring my newborn baby. I got SA last month. The application is in process at Manila VO right now.
For translation, it costs 4000-5000 yen in japan for each documents. Certificate of translation from the translator with signature is acceptable.