I have the same question but for the US citizen child. My friend has B permit but submitted for renewal. She plans to obtain 3 months "visa de retour" to fly to the US, have a kid there and bring it back (she is trying to avoid to have her husband with whom she is separated to know about the kid she is having from another man!).

So, does she have to apply for the residence permit for the newborn in the Swiss Consulate in the US (and if yes, how much time approximately does it take to get an answer?) or she can bring him to Switzerland and then apply for the residence permit in Switzerland?