I've asked this question numerous times and no one seems to know. Here is the info I have gathered:
-There is a U.S. aftermarket seat company called Carbeau that sells very nice seats (in leather too). This is the company you want to call because they have also designed adapter frames to mount their seats to your specific application.
-Another option is to rebuild you current seat with a new box spring and seat pad. I went this route and it cost around $250 just for those two parts. The new seat frames bottoms are a lot more firm and don't sway from side to side. The drawback to this is that you still have a mediocre seat - no modern lumbar support, so side bolsters on the seat or back, no option for heat etc. You can get all this with a Carbeau seat.
-I have been on this board for a few years now and have never seen anyone install different seats in a w123. On the other hand, there is (was) a guy in the Vintage section who swapped in seats out of a w140 into an old 260SE. I think his car was something like a 1973 model. He sounded like a really handy guy, so he may have done some custom work to make them fit. I emailed him about it once and never got a response.
-My big concern with custom fitting seats (even the Carbeaus with the company mount) is that the w123 seatbelt buckles to the frame of the seat rather than the frame of the car. Are you really safe if you attach the seatbelt to something else or in some other configuration? I don't know, but the thought concerns me.
Bottom line, anything is possible. Carbeau is the only non-OEM path I could find. I have never seen or heard of anyone install seats out of a w124/126 into a w123. I know that the the seat mount on my w124 is different than my w123. And lastly, there is something to be said for keeping the car stock looking.
Good luck, and I hope this helps.