I am assuming that the existing floor has no insulation at all and that you live in a place that isn't terribly cold in the winter, otherwise you would already have insulation. Also, I am assuming that the bottom of the floor joists are so close to the ground that a person can't crawl in there. If you have enough space and access, you could try to use some 2" thick insulation sheets and attach it directly to the undersides of the floor joists.
This would be plenty of insulation, as this stuff has very high R values. It is made from poly iso cyanurate foam and it comes with shiny foil on both sides in 4'X8' sheets. If you don't have enough room for nailing it with those funky nails with the huge plastic washer heads, then you could maybe use some braided "aircraft" wire that they sell at the hardware store. Attach the wire to one side of the house about every 2' using galv. eye screws to the outside band joist and lay the wire under the room on the ground. Then put the sheets under the house on top of the wires. Then tighten and attach the wires on the other side of the house and secure with more eye screws. YOu might need those small turnbuckls that they sell for this type of wire in the hardware store to tension the wire. The wire is fastened to the eyes by putting it through the eye and then twisting it back on itself many times, or by using double crimps that they sell for this "aircraft" wire. You will need to tighten the turnbuckles after a few days or week when the wire takes its initial stretch.
I know this all sounds a little screwy, but if you have enough access to accomplish this, or something similar, then it sure beats pulling up your floor etc. and you still have ventalation under the house.