First: ALWAYS and I mean ALWAYS clean out old lubricant before applying new one!!!!! I can't stress it enough. As far as I've been taught, not doing so wears out components and fast.
For your application I would go for ol' trusty white lithium grease. Don't use too much, a dab will do. Overoiling has never solved anything. I use lithium mostly on my skateboard bearings and that stuff is wonderful.