Zener Diode Selection for Relay
How to choose

The first part is consideration for the instantaneous power dissipation:   \$24 * 80mA\$  As long as your Zener can handle that it will not die immediatly.

The next is the total energy.

The Inductance is key here &amp; to a lesser degree its resistance.

The use of a zener ensure a constant voltage during decay as oppose to an exponential if it was to naturally decay via a freewheel diode &amp; the coils own resistance.

\$V = L\frac{\Delta i}{\Delta t}\$
V = Zener Voltage
L = coil inductance
di = 80mA

Leaving dt

Now you know the energy stored in the coil: \$E =  \frac{1}{2}Li^2\$.  This energy needs to be transferred from the coil to the Zener.

With the time required from the previous calculations you now know the total power that needs to be dissipated \$P = \frac{E}{\Delta t}\$

With the power for one dissipation known you can then start short listing Zeners

Finally ... duty. Do you want the zener to be chosen such it can just handle one discharge event and then takes time to cool or do you need to tolerate a minimum enable-disable duty. Equally how many short succession enables-disables.

This increases the rms power that the zener needs to tolerate