typically on vinyl you can get away with a diluted degreaser/all purpose cleaner and a medium stiff brush to remove any dirt/grime.
after they're cleaned a water based vinyl dressing would be the way to go. I work for a chemical manufacture and can help you out, but lets keep that offline as I don't want to violate vendor policies here.
I've acutally setup more than a few golf courses with a program using our APC and Vinyl product just for keeping their carts nice for members. You can shoot me an email if you want and I'll give you some pointers.
dylan.vonkleist@gmail.com
Again - if this is beyond the site rules or stepping on any toes mods - please let me know.