I guess it also depends what language you need the birth certificate translated to.. when we got our little ones official full birth certificate (from the commune office - costs CHF 10 or 20) last year, it was already in 5 languages: french, german, italian, english, and if I remember correctly, spanish.
Sweti is correct, the requirements for getting a permit for the baby differ depending on where you are from. Ask the cantonal authorities, but will most likely include (this is what we needed):
- your full birth certificate
- your wifes full birth certificate
- your marriage certificate
- attestations de domicle for both you and your wife from the commune
On top of that our documents had to be less than 6 months old, and all be Apostille certified.
But it looks like you already know all of this: Newborn Birth certificate & Permit
P.S. The process we followed was
1. Get full birth certificate
2. Use certificate to apply for citizenship from "home" country
3. Apply for passport from "home" country
4. Use passport to apply for Swiss permit.
We had as many documents organised and certified before birth as possible and all up it took just under 3 months.....but it took one full month of that waiting for the official full Swiss birth certificate!