Is the vinyl top a convertable type top or is a hard top with the vinyl covering?
Have you tried anything so far other than soap and water?
It is a hard top covered with vinyl. I have not tried anything else besides soap and water, yet. Hoped you could save me some trial and error.
I would not go with bleach because of the effects it can be adverse on the paint job, but there are a couple of things I have found work very well to clean vinyl.
The first is the Mr Clean Magic Eraser: http://www.mrclean.com/en_US/magic-eraser-extra-power.do I have used this on vinal and leather to remove some hard to get out stains created by a teenager.
The other suggestion that works very well is an old stand by for cleaning. It is Comet Scouring Powder and a nylon scrubby. The combination works great for cleaning the type of staining you have described. What I would do is a small area and rinse doing this in sections. Bleach and other cleaning materials can affect your paint on the car and using the Comet makes it where the job can be done where it does not affect the paint and can be washed off easily.
Once the vinyl is done I would get a good Vinyl protectant on it. McGuires makes some great auto products.
There are also vinyl cleaners that are sold in Automotive supplies, but the Comet, scrubby and elbow grease seems to work well.