Halogen-substituted aliphatic hydrocarbons are usually miscible with oils. Pick the compound by its density, price, safety, boiling point and other characteristics.
For example, trichloroethylene (trico) has a density of ~1.6 g/cm3, and a Material Safety Data Sheet shows a vapor pressure of ~60mm Hg at room temperature and a time weighted average (TWA) toxicity limit of 50 ppm (269 mg/m3) from ACGIH and OSHA. Though it's readily available, trico might be too toxic and volatile for your use. A similar chemical is tetrachloroethylene, sold as "perc", with the same toxicity issue.
In general, going down the halogen group increases density, so bromine or iodine substituted compounds would be denser than those with fluorine or chlorine.