I'm not sure about a tack shop specifically but I do recall seeing tack supplies at the Qualipet in Pratteln .
I believe the 14 tram goes out that way or you can take the bus (the 80 goes out that way too, we had to take it home from that Ikea once) or the train, I'm unsure which train to take though.
I'm sure you've tried - but I've found the internet a wealth of information. I've been near Lausanne for a week now , and the hunt for a riding stables has begun (I'm considering bringing my horse over from the UK in the spring).
I found a list of all stables in french switzerland ( http://www.handicheval.ch/Corps/Chev...sse/manege.htm ) - something similar may exist in the Basel area? I've also found a few places from driving round (I'm guessing not an option for you). I am yet to brave going in to a stables though as my French is appauling (lessons start next week)....
Quali-Pet does indeed have an equestrian section, prices seem high (surprise surprise, a good 30 - 50% up on London!)
If I remember correctly there's another one near SBB station on Gueterstrasse - leaving it out the back past Media Markt and then turn right towards Zoo. Not sure if it's still there though.