You say you are running on an engine stand? Do you have all the rotating mass on it like clutch or convertor? That all adds to the flywheel effect which helps the motor keep running smooth at low speeds? Of course a vacuum leak will make idle rough too. Do you have all the ports on the carb/manifold plugged or hooked to an appropriate working device?

Why are you running it on the engine stand?

Yes, you need the torque convertor!!!! That is the largest portion of the flywheel weight.

You don't say what carb you're running, but if it's a holley, there's an adjusting screw for the secondaries. If it's open to much you'll get a rough idle that can't be adjusted out. A simple check is turn your idle needles in and see if that affects the idle. If it dies when adjusted in, then you're on the idle circuit and it is something else. If there's no or little change, try adjusting the secondaries. If you've had to adjust the linkage screw in to maintain an idle, the secondaries may need to be opened a bit to bring it back to the idle circuit. This is assuming the above doesn't help and the engine is up to operating tempatures. It's a whole lot easier for me to think about this than it is to type it so it makes any sense.