Do I need a birth certificate?

I was born in Taiwan and am a naturalized U.S. citizen. I applied for a visa at the Chinese consulate in San Francisco. They require a birth certificate, which I cannot locate and produce. I have successfully applied for a visa from the Chinese Embassy in Tokyo in 2002. I was advised to bring old passport and apply back in Tokyo, where I live. Are they going to ask me for a birth certificate when I apply in Tokyo, or will the old passport with the old visa, suffice?

Also, with the expedited service, is it possible to receive the visa on the same day? Thank you in advance.