Sure. If your child lived in another country then you can use his current or previous passport as proof, or you could use his school records or how employment records in that country. Any document that shows your child lived in another country for an extended period of time would work.
You said at the beginning that certified copies are accepted, what about notarized copies?
Notarized copies are not accepted, only originals or certified copies.
And, what other documents, besides the normally aked ones, I can use as my child's proof of identity?