Thanks for all the replies. I've measured the draw of my Mega 1280 board and it was down around 12mA, idle. I didn't know if the act of programming might make that spike or not.
As I said, I'm using a 9v battery to power the target board. I have some LM317 and some 5.1V Zeners to choose from for a voltage regulator. I know they'll waste a little power, but if it only draws 20mA... a 150 ohm resister in series with the zener will keep the resistor under 1/8 watt. An auto-shutoff circuit is probably in order.