You could also consider to add that zener to the flyback diode.
The flyback avoids a spike upon opening of the relay. But it does so by shorting the coil and keeping voltage low, so it takes a while before the coils energy is dissipated. (energy is volt times amps times time) If you add a zener of reasonable voltage, voltage will be higher, more energy is dissipated faster.
The relay will open faster, not only improving response time, but also increasing the relays lifetime.
See
this simulator (wait a sec to start, allow Java)
You can switch on normal diode, zener pair, or nothing.
Added considerations:
You need to select your zener not too high: while it will avoid a negative high spike, but will still cause a negative smaller 'bumb' on the supply side. So consider what the driving components can handle.
You need to select your zener not too low. No diode at all will switch immediately, a diode means the relay contacts only slowly switch, the higher the voltage, the faster the switch. If there is no electronics involved, and you are connected to some lead-acid battery, consider not using a diode at all. (fastest switch time)
For industrial/automotive/marine mounting, I often use 2 zeners (so polarization does not matter and its easier to screw under relais terminals) a bit above max supply voltage. So 32V for a 24V battery system (seeing as how a charge can be up to 28.8V. (but as stated this is not needed at all if directly connected to the battery bank)
But on a PCB, where no mistakes in polarization can be made, and negative voltages can be a problem, I guess a zener plus normal diode would be better, as you can select any voltage that you think is acceptable.
PS: you still need that resistor! The zener addresses a different item. Best place the resistor between the (zener)diode and the coil, so it helps with the power dissipation.