new birth certificate abroad?

If US citizens living abroad adopt a child from abroad, do they get a new birth certificate issued? If so, who would issue that birth certificate with the adoptive parents' names on it? The US consulate? If you can/do get a new birth certificate issued this way, is that all that is then needed to get a US passport for the child? I'm just thinking of a situation where a family lives abroad and adopts following the laws of the country they live in, and later decides to move back to the US. That can't be considered an international adoption, right? So the normal requirements for a visa for the child wouldn't apply, right? Wouldn't the child have US citizenship then by virtue of having 2 US parents listed on their (revised) birth certificate? Or do other countries not issue new birth certificates, only adoption decrees? Thanks so much for your insights on this!