This is an easy update until I decide if or when I want to buy new door knobs.
Spray paint really can do amazing things and in a quick and cheap way. It can be a temporary or permanent fix depending on the project and a can of spray paint costs around $4.
First I removed the door knobs using a screwdriver. I kept the door knob sets together. Then I sanded the knobs with 400 grit sandpaper. This is to lightly rough up the surface so the spray paint adheres better to the door knobs. Wipe to clean the door knobs after sanding. You can use a degreaser to clean the knobs if needed.
I punched holes in a piece of cardboard to set the knobs up to easily spray paint them. I did this with both knobs and the screws. Then I spray painted several light quick even coats allowing them to dry between coats.