I have used this really dumb technique quite successfully with garage floor oil stains:
Cover the stain with a layer of Oil-Dry, soak the Oil-Dry with 100LL aviation gas (which dries with no residue). Let is soak a minute or two on the stain, then brush the mixture back and forth a few times with a broom. Scoop the wet Oil-Dry up with a nonsparking shovel and put it in a garbage can outdoors until all the avgas has evaporated. For a solvent you could probably substitute acetone, lacquer thinner, etc. for the avgas. The key is a solvent that dries with no residue.