You could try American Science & Surplus.
They might have some carbon rods.
It's sort of pot-luck, they have whatever they can find on closeout or surplus, but back in the 90's as a kid screwing around in my garage, I got the carbon rods there when I made an 110V AC arc-furnace out of a terra-cotta flower pot, and some curtain rods, and a salt-water/lead fishing sinker rheostat.
The design was from an old 1950's "Jr. Scientist" book, back when liability was the assumption of the experimenter, not the publisher.
It worked great until I got the idea to use a wall dimmer rheostat, instead of the salt-water/lead one. It worked for a few seconds, then promptly melted, shorted across itself, and blew half the breakers in the house... :candle:
At least summer vacation was interesting at my house.