I have a couple small tubes of grease I got with my Penn fishing reels. It is light and very slick. I lubed my cylinder pin with it and it's slick as snot. I was wondering what everyone else used. I assume whether or not it's petroleum or not doesn't matter since it shouldn't really be affected by fouling.
I use a light coating of Ballistol. Better than that was Tetra, but I don't carry it with my muzzleloaders, so I don't use it anymore. I never had good luck with anything thick or grease like. It seemed to attract more fouling and bind sooner. That might be because of the dry climate here and the dust. Grease seems to attract dust like a magnet.