Have a look for something called "ethernet UTP to Co-axial tranceivers."
Way back in pre-historic time, ethernet used to be base on co-axial cable before UTP became popular. However, there's a few caveats:
Ethernet over coax was terminated onto BNC plugs (there were rarely any sockets as offices tended to just "snake" the coax around the building from station to station to station as required) so you may need to figure out how to terminate you cables onto BNC as such tranceivers probably present onto BNC.
"At the time" 10mbps was the de-facto speed and 100mbps was new and "fast" (it was actually called "fast ethernet") so you may not find any 1000mbps (AKA gigabit) devices.
Ethernet over coax uses a "common bus" paradigm - you can connect multiple "drops" off the same cable runs, but all the end station (or tranceivers in this case) function "Half Duplex" which means they have to compete for available bandwidth (as Wi-Fi and Homeplug still do.) So 100mbps Half Duplex isn't going to be fast. Worse, if it only comes up at 10mbps.
The tranceivers may need power from somewhere - possibly some kind of "wall wart" PSU.
And their may be electrical reasons it won't work - electrical engineering colleagues may have something to say about the impedance and so forth of the co-ax we used to use for ethernet versus TV coax.