Mix up some trisodium phosphate and water. Trisodium phosphate, or TSP, is sold in home improvement stores and janitor supply stores, and boasts the power of highly concentrated chemicals for difficult cleaning applications. The label should state how much water to add, but, in general, you should not need more than 1/4 cup of TSP per gallon of water.
Pour your TSP solution over your cobblestones and ensure that the liquid fully covers the oil stains. Put on a pair of rubber gloves and scrub the stones with a firm-bristled brush to loosen and remove the oil residue.
Rinse your cobblestones, using a pressure washer or hose with a fine-mist spray nozzle. If no oil stains remain, you can call it a day. If you still see traces of oil, proceed to the next step.
Mix a solution of 15 parts water and one part household bleach. Bleach is a powerful irritant, so wear your rubber gloves while mixing and working with the solution. Pour the bleach over your cobblestones and immediately scrub with a firm-bristled brush. Bleach is more powerful than TSP, but also more corrosive, so use it as a last resort.
Rinse your cobblestone driveway one last time with your pressure washer or hose. If you have grass or plants surrounding the cobblestones, water them before you rinse the cobblestones. Bleach runoff can kill dry grass and plants.