I have a vapor barrier on the dirt floor already. The insulation will go in the floor joists above, paper side down.
"When fiberglass batts are installed in the ceiling of a crawlspace, gravity always wins in the end" source
Faced or unfaced, it is almost always a bad idea to insulate the floor above a crawlspace, especially with fiberglass batts. Insulate the crawlspace walls and seal the vents instead. The one exception is if you are in a flood zone.
A sealed crawlspace will be drier, healthier, and usually more energy efficient than one insulated at the floor.
The problem often overlooked is that the paper vapor barrier on the insulation should be oriented to face towards the room. Also, the paper must be in complete contact with the floor bottom to function correctly. So now the only way to secure the insulation in each joist bay is with metal push rods. Try to fill each joist bay fully and completely.