This station was opened in 1863, at the same time as Lawrence Hill. It was built to serve the line from Bristol to South Wales, though, ironically, those trains do not stop there any more, only trains on the Gloucester and Avonmouth lines. It was expanded to two platforms in 1874 when the line to Clifton was opened, and to four platforms 17 years later in 1891. It quickly became a major station in the Bristol area, in particular for trains which did not stop at Temple Meads. Nowadays it has regressed to two tracks and all the buildings are gone.
(Thanks to John Rogers for the photo)
Here is one of the Gloucester trains stopping.
The most notable thing about Stapleton Road station now is the artwork on one of the walls. Isn't that W.G.Grace with bat in hand?