Cheap source of clock: Goodwill, Salvation Army, Dollar Stores...
Diodes: Radio Shack 276-1103 (1N4004)
Resistor: Radio Shack 271-1325 (2.2K 1/4W)
Capacitor: Radio Shack 272-1024 (4.7uF/35v)
I substituted an easier to find capacitor, but note that this one is polarized and must be installed with correct orientation.
Modified schematic attached.
What I have done for mounting small regulator circuits, when using a cigarette lighter plugs is get one of the car-charger cords for cellphones, again from Goodwill, and gut it. Install my regulator inside it. Wire that to a dummy battery, to fit in the clock, made of a wood dowel and a couple of small screws.
Ken