Should I try changing coils spring s?

My new used car has been fishtailing over bumps. A couple mechanics couldn't find anything wrong in the suspension. The dealer put in new rear shocks as I bought it and that helped a lot, but only for a few weeks. Now it's back. I had a fourth place check it, a tire suspension place, and they said my coil springs are loose. That changing those would help fishtailing.

My own mechanic went to go do the repairs for me but checked first himself..said you can't tell if springs are loose on a lift. That he can do it but can't guarantee that it will correct the fishtailing. My last option would be to bring it to the actual dealer/make of the car (original small place I bought it is out of warranty), and have them diagnose and repair it..but of course I'm sure the price will be much higher than trying the springs with my own mechanic.
Would you try the springs repair?