I have never been successful getting mold stain out of cloth without using bleach. Of course, if it is a colored fabric, using bleach will bleach the color.
I would advise you, though, to make a detailed inspection of the car seat. The plastic can become brittle over time making it unsafe to use. This can be caused by the extreme heat and cold they experience while sitting in the car (and possibly in storage). I've seen a lot of car seats today that have expiration dates on them because of the plastic.
I passed my infant car seat along to my sister who had a baby a year after my son was born. Thankfully, before they used it, my BIL inspected it and found it to have a crack in it.
You are also suppose to get rid of a car seat if you have an automobile accident, because its integrity can be compromised.
It is also not advised to buy a car seat from a garage sale or thrift shop because you don't know where it came from or what it has been through.