Sure, no problem. The documents you are being requested, are meant to prove your child is a U.S citizen, so you can effectively get a replacement card.
That's mostly in cases where child's citizenship has not been established beforehand. Is that your case?
Yeah, i haven't established my child citizenship yet. What should i do, then?
Good. In that case, we need to see proof of child's U.S citizenship, through certain documents, such as U.S birth certificate or U.S passport.