Yano, I was gonna post this on the LeMons forum because so many people believe a $500 Miata can't be had...
But a friend of mine just snagged a '95 in decent condition for $500. Some minor fender damage, blown clutch slave, typical Miata oil leaks and not running due to a dead battery. Would have been the perfect LeMons car... sell the nose piece for $150, the rear finish panel for $50, tail lights for $50, front signal lights for $50, misc interior bits for $50. With all of that, you could afford to put a new set of GR2 shocks on it and even be honest about the minor maintenance costs required to make it uber-reliable.
Just keep your eyes on Craigslist, something juicy will come up. BMW, Miata... hell, just about anything that's common, reliable and decent-handling would make a good LeMons car.