My brother was born on a U.S. military base in Japan. Both of my parents are American. When he first traveled abroad, he was required to get a certified copy of his birth certificate from the U.S. State Department in Washington, where they keep the records. Check the U.S. State Department website and call them. The snail mail way entailed a call requesting an application, receiving the app, completing and submitting the app along with a check for the certificate. From the initial call to receipt of the certificate it took four months! Perhaps you can download the app and fedex. I believe there is a service to expedite the processing time for a fee. Not sure about that. Better hurry!
I can't imagine why they would need the passport of one of your father's parents. His birth certificate should state his parents' nationality.