I did this last Summer using a rustoleum flat black spray paint.
Use a soft towel and clean the oxidation off of the handle and frame with alcohol first. Dries up in just a few minutes. I had a few small rust spots, so I sanded them down from 120 to 200 grit and then cleaned them up.
One thing that made it easier was to tape off using 2"-3" scotch blue painters tape. The wider tape made it easier to work with IMO, but I was also able to slide the tape behind the edges of the door handles. Mine were just loose enough to do it and it assures you of much cleaner lines with no chance of overpaint. Easy and good looking mod.