Noise Coupling methods to communication cables
Magnetic coupling injection: -



Picture taken from here.

Capacitive clamp coupler: -



Picture taken from here.

For differential injection of a voltage in series with the inner conductor in the coax I would use a high frequency, low impedance pulse transformer with the secondary in series with the coax inner conductor either at the feed end or the receive end. Something like this should work: -



The basic idea is that the transformer injects across a low impedance in series with the coax inner cable. You can probably use something as low as 1 ohm as the injection impedance so that the transmission line termination impedances are not unduly affected.

In principle it's the same as this for testing power supply noise except the power supply is the data system: -