There's quite a few in Amman @Al Burgan Handicrafts @Jordan River Foundation Showroom @Safi Crafts @Silsal (not so much handicrafts but they do have beautiful ceramics and other items for the home), @Wild Jordan Center and then there's the balad of course.
Check out @Safi Crafts all handmade crafts as well as @Khordda which reuses material they make wonderful things and great souvenirs cheaper than Afghani and great for the Jordanian community!