Checking maps on the Scottish national library site doesn't indicate the stations either, but Biddulph station itself was closer to Bradley Green than the centre of Biddulph.
Childerplay seems to be no more than a farm not far from Black Bull station but there doesn't seem to be any place with the name Black Bull. There is a Public House marked close to the station called 'Railway Hotel', perhaps it was previously called the 'Black Bull'.
Checking Quick again, he says Black Bull was in Bradshaw as Black Bull Childerplay from 1873 to 1886. He also says according to the Railway earing House the station was renamed from Black Bull for Biddulph & Chell to simply Black Bull from 1 May 1897.
His entry for Biddulph says the station opened as Gillow Heath and was renamed 1 May 1897.
Seems like neither Childerplay or Bradley Green were additional stations in their own right.