The fuel burned by container ships is literally the sludge left at the bottom of the distillation vessel after all of the lighter petroleum fuels have been removed for sale. It is incredibly cheap fuel, extremely energy dense, but unbelievably dirty stuff.
Unfortunately, these ships only burn the nasty fuel in international waters so the process of getting them to pay for emissions would have to go through international maritime law, specifically MARPOL [1]. If you want an idea of how difficult that would be, check out the implementation and enforcement section of that page.
[1] https://en.wikipedia.org/wiki/MARPOL_73/78