Marcel,
The functionality of the DRV120 should not be affected by the inductance of the coil. I did some tests in the lab today, and did not see any issues with the output waveform. I used the DRV120EVM for testing and supplied it with 24 V from a bench power supply. For these tests, I used ~200 Ohms for the OSC resistor (adjusted with potentiometer). The device on the EVM board is the DRV120A (14-pin version), so I was able to adjust the peak and hold values. I found that if I increased the HOLD current, that the audible ringing of my relay would get quieter, so that is one thing you can try to reduce the ringing, but it will mean you need to use the 14-pin version instead of the 8-pin.
This scope shot is from a relay w/ a coil measured at 600mH and 660 Ohms. The current profile is in green (20 mA/div), and the OUT pin voltage is purple.
This scope shot is from a solenoid measured at 20 mH and 11 Ohms. The current profile is in green (50 mA/div), and the OUT pin voltage is purple.