"The Manchester South Junction & Altrincham Railway" (Oakwood Press - 1994 edition) has the site of the original Cornbrook station (01JUN1856 - 31MAY1865) as being on the South side of Cornbrook Road between Cornbrook Road and the site of the former Cornbrook East signal box.
Approximately where Ogden Street appears on the later 1890s map extract posted upthread by
@LNW-GW Joint.
Looks only to have been alongside the running lines to Castlefield Junction, not sure if the parallel route into Manchester Central would even have been built by then.
The present day Metrolink Cornbrook station is, of course, built on the route of former line into Manchester Central, and is on the other (North) side of Cornbrook Road.