If you include the stations such as Cockett, Swansea Bay, Upper Bank, Landore, Mumbles Road and Morriston, which have always been areas considered as part of Swansea (at least during my time), then there were at least 9.
I believe that the Rhondda and Swansea Bay had a station or two on the east side of the River Tawe at one point as well. I won't include Gowerton since that magnificent place once had it's own court, so I've always considered it to be separate to Swansea!