Sounds like a classic vacuum leak. A small leak is not material at speed because its percentage of the total air volume is not significant BUT at idle that same leak will cause misfiring due to too lean a air / fuel ratio.
Possibilities: anything that's vacuum powered, cracked broken or disconnected vacuum hoses to the intake manifold, intake manifold gasket. Listen for a hissing sound at hot idle.
Very CAREFULLY apply propane to suspect sites and KEEP YOUR FACE DISTANT. A leak will draw the propane into the motor and it will run smoothly, then cut the propane and the rough idle will return. BE CAREFUL - propane can flash!!!