Julia, first welcome to the MMI Afourian Forum.
Stalling at idle can be a few things and the sooty plugs do narrow down the issue.
First a couple of questions, first how long since a tune-up~~IE points, condenser if so equipped. Is it a std (stock) ignition or electronic. Second how old are the plugs?
A quick thing to try is to lean the carb idle down a bit. This is done with the "idle air screw" on the topside of the carb. Try turning it "out" about a 1/2 turn (counter clockwise) to add more air and that will lean the mix a bit. Might help. Also advise if it does or not.
Any other things you have noticed like lack of power, rough running or harder to start?
Dave Neptune