I had never heard of a snubber before (at least not in the context of circuits). Reading around it seems like they are used to prevent arcing at switch contacts. But is the NE555 relay a solid state device? And, if so there aren't any contacts and a snubber wouldn't be needed?
Or, if it isn't solid state can somebody tell me which diode to use in the circuit? And I assume it's wired in parallel between the 2 wires coming out of the solenoid?
So there is no confusion, a general purpose diode has two terminals (or wire leads). One terminal is the "anode" and the other is the "cathode".
The diode is usually marked with a silver or white band around one end of the body. The band identifies the "cathode".
Reverse connected means that it is connected so that no "forward" current flows. So a reverse connected diode (or snubber) has the band connected to the positive side of the coil, and anode connected to the negative side of the coil.
The coil of a solenoid is a type of inductor and an inductor can store energy when energized. When the coil de-energizes, its magnetic field collapses and releases the stored energy in the form of a short electromagnetic pulse. The pulse can interfere with the operation of (or damage) solid state electronics. The "snubber" diode will short circuit the pulse to ground where it can do no harm.
The diode allows the inductive solenoid current to keep flowing when the controlling switch is opened, until all the inductive energy is dissipated in the diode and solenoid resistance, instead of at the switch.
A typical one I keep on hand that covers many low power eventualities is the 1n4007.
If the coil is high power/inductance you will need a higher current value.