Do you have a gas range in the kitchen? If you do, you have what you need close at hand.
As for the buzzer idea, it is the repetitious opening and closing of the coil via contacts that create the miniarc at the contacts. Lenz's Law (for NN4RH's benefit - hi Ron) or simply the voltage produced by a rapidly changing magnetic field is - L di/dt. When time approaches zero, well, the voltage approaches ...... the sky.
You can devise one very simply, if you have a junk box with an SPDT or DPDT 120VAC coil relay. Simply connect a set of the normally closed contacts in series with the coil and you have, depending on the size of the relay, quite a spark gap machine. Just don't connect an antenna to the contacts... :-)
You could do a similar thing with a small SPDT DC coil relay, but only half the fun, unless its a big one.
To take it a little further get an old automobile spark coil and connect the primary in series with the buzzer, other end to ground (negative terminal). This will make a potent spark using a 9 volt battery and since you will only use it for a few seconds the battery will last quite a while.
Another way would be to get a large electrolytic capacitor and simply charge it up and discharge it through a carpenters pencil lead. That will make one heck of a spark. and arc actually for a very brief period much like lightning.