My first thought would be to use a semi-rigid spray foam, such as Icynene. The foam sprays on, preventing infiltration-causing voids if done correctly, but the surface allows moisture to go through it because it is porous. The company claims that the moisture will not cause mold or rot the insulation.
If your stone foundation is not decorative or you can do it subterranean-only, then waterproofing it from the outside is preferable to allowing the moisture to infiltrate in the first place. For that I would use a system that includes waterproofing, drainage board and a filter fabric such as Miradrain. It is important to install these systems exactly as required by the manufacturer or you can destroy the waterproofing capability.
An alternative to completely waterproofing would be a gravel drainage channel with a perforated pipe or "french drain."