Here is a simple power supply based on a single car ignition coil driven by 120VAC through a 600W dimmer control and a 3uF AC motor cap. It makes a continuous arc about 1/2" long. The coil can run like this indefinitely. I detected no warming at all. I've included a simple hookup diagram. Let me explain the circuit. I put the dimmer switch and the motor cap in series with the black "hot" line and hooked it to the (-) terminal on the coil. I hooked the white "neutral" line to the (+) terminal. The green ground wire from the dimmer switch goes to wallplug ground. Spark output is between the center terminal and (+).

This power supply should do fine for a very small tabletop Tesla coil. See the output arc? Not bad for such a crude setup. It took me about 10 minutes to assemble it. For Europeans and others, this setup works just as well with 240V/50Hz current. I've experimented with AC motor caps as little as 2uF and as big as 30uF. They all worked, but the bigger the cap, the greater the output power. If the cap is too big, the ignition coil will overheat. If the coil body gets too warm to comfortably hold in your hand, you need a smaller cap.