How should I use fiberglass batts to insulate between floor joists over a stone basement?
Buildingscience.com has a decent article that covers a very similar situation with floors over crawlspaces

The two key points with this:


One vapour barrier, so as not to trap moisture. Essentially, drying happens on both sides going in the direction away from the vapour barrier, and if you use two barriers you're trapping moisture which leads to mold and rot.
Condensation happens when warm meets cold. When you're using batt insulation, you want the vapour barrier on the warm side so you're not getting condensation (and thus water) on the insulation. 


The situation that most closely matches what you're talking about recommends this:



The rigid foam on the bottom of the joists is your vapor barrier: it must be impermeable and this means that the connections between sheets and around the edges must be sealed too. Even though the vapour barrier is essentially on the outside of the batt insulation, because the foam has an insulating value (unlike 6mil plastic) you don't have warm meeting cold here and won't get the condensation problem.