Have you received their finger print notices yet? I am still waiting but according to some people, parents' finger print notices should arrive in 1-2 weeks.
You can ask your friend to check with the (天津)市公證處 first to see what documents they need to issue the birth certificate. In my case, ID + 戶口本, and since the grandparents passed away, they need a document from Police certifying they have diseased. Different city may have different policy.