Do we need any kind of protection for AC relay coil?
It's not unusual to switch one relay with the contacts of another with no "protection". You can add an RC snubber (typically something like 100 ohms in series with a few tenths of a microfarad) across the contact or across the coil to reduce EMI and sparking. 

Such a snubber can also be useful across an inductive load. Or across the coil to prevent high dv/dt at turn-off from preventing commutation of a thyristor (if you are using an SSR, it will often be built into the SSR). 

Sometimes MOVs (Metal Oxide Varistors) are used, but I would suggest not using them for such repetitive transients as they actually wear out over time and still allow rather high voltages and don't reduce dv/dt signficantly. If you must use them, take into account their eventual failure mode (usually shorted, followed by a certain amount of flames and smoke and then opening up, if they are across the power).