Hello again,
Here is how I would do it: It assumes that you want the relay pulled in when the 555/6 pin 3 is high.
If the relay coil resistance is less than about 15Ω, the 2N2222 may get warm to hot. I prefer the NFET switch. Any Power NFET capable of switching > 2A, with a Drain-Source breakdown of >25V, and a Gate-Source Breakdown of > 20V would work. (IRF530, for example).
The Snubber could be a 1N400X.
The resistor to the base of the 2222; Rb = E/I = (12-Vbe)/Ib, where Vbe is about 0.65V for a 2222.
Ib=Icoil/β, where Icoil is the relay current, and β is the current gain of the 2222.
Halve the computed value to guarantee saturation when the 2222 is turned on.