Craftsman With CV15S rough idle, replaced carb, still there

Hello All,

I have a craftsman Mower with a Kohler CV15S that i picked up for free from a friend. I got it running but it surges at idle and blows white/black smoke. below is what i have done

Cleaned existing carb and rebuilt - problem still there
New plug - problem persists
Gas in oil - changed oil and replaced carb - problem persists
put an in line shut off on the motor and when i just slightly crack it, it runs great until it runs out of fuel

I don't understand why a new carb would not have fixed it???? I have a new coil on the way but im nt sure if im shooting in the dark with that...

Can anyone help me???