Bleach & water in a spray bottle. 1 part bleach to 10 parts water. This should not discolor nor harm the vinyl. Good luck!
It could also mean that there is a inside leak in the house or the gutter and downspout are not draining properly or leaking down the side of the house behind the siding . You may need to do a water check by spraying water on the roof and in the gutter to see if the water is going behind the siding. Www.stretcher.com/stories/03/03aug11a.cfm
You need to use oxygen bleach solution which should remove the stubborn stains with ease, and it won't damage your vinyl siding. Many bleaches can make your vinyl siding brittle and fade.