Diamond stones are pretty much fine with anything you want to use. In a pinch, use them dry but wipe off the metal dust frequently (dry rag). In the shop where I don't have a sink I use a spray bottle of isopropyl alcohol (50% seems about right). In the kitchen I use soapy water. I've seen oil used but I'd rather not have the mess.

Diamond stones don't absorb so any liquid that can be cleaned off and isn't corrosive or otherwise dangerous will work.