I had a similar problem with my Onan, it would crank for a long period, fire then belch black smoke and sputter. When it warmed up it would run fine for hours. If I manually operated the choke it would start immediately and not sputter or belch.
The problem turned out to be the choke membrane had a hole or tear in it. I replaced just the choke and it has worked fine since. Now the bad news, I went to my local Onan rep and he couldn't order just the choke, I had to buy the whole carburetor for something like $250.00! Well after I whined a bit he agreed to remove one off of an old carb he had and sold it to me for $25.00, I did the work myself. It's been running fine for more than a year.
Paul - WA1IWH
Margaret - She who must be obeyed.