I installed a small 50 watt-per-channel amp under the dash of my '60 Fintail many years ago. Purpose was to deter theives by keeping my mono Becker visible in the dash, while driving a pair of two-way box-speakers mounted out of sight, below-behind the front seats. To the amp's input sockets, I cabled the headphone output from a Walkman or portable CD player, resting in the center-tray.

As for the W123, I've had the seats out of a couple of my 240Ds to fix the floors, and I'm considering adding an amp to my 300TD

A large amp won't fit under the dash or rear seat on the W123, so your best bet is under the front passenger seat. There's the added height adjusment mechanisim under the driver's seat, so I don't think an amp or subwoofer will fit there.
Without seeing the actual components or having their measurements, I don't know if an amp and subwoofer would both fit together under the passenger seat. I don't know if it's even OK to have them operating next to each other. You may have to install one of those components in the trunk.
However, on the W123 sedans, the fuel-tank is between the rear seat and trunk, so that's an added obstacle to mounting something back there.

As for mounting something under the front passenger seat without drilling holes in the car, you could fasten a steel strap across from the seat's rear mounting-bolts, and attach the amp or subwoofer to that.

Happy Motoring, Mark

__________________
DrDKW