Is it possible to paint stainless steel door knobs?

yes, remove from the cabinets and spray paint them with Rustoleums 2X for metal

Buy a can of rustoleum spray paint and a cheap knob and try it. If it works then remove all the hardware and spray away. Probably several light coats will work better and cause fewer drips than a single heavy coat. Be sure to use in a vented area on newspaper or drop cloth.

Rustoleum makes a spray primer for metal. I would remove the knobs and spray them with primer. After the recommended dry time, use gold spray paint for metal and let them dry. I would also follow-up with spray polyurethane for protection.

Nothing will stick unless you first sand them.

No need to prime! Just lightly sand to remove any gloss. Then spray paint with Rust-Oleum paint made for metal. Several light coats will get you a smooth finish. Let each coat dry.

Changing hardware can be expensive, but if gold is what you want then buy it. You don't say what color of the cabinets are. Call Homedepot or Lowe's paint department and ask if gold can be painted over stainless steel. Maybe if you sprayed it on, then you might need primer

...changing the hardware is such a pain because of the “holes”. I can never find hardware that matches the existing ...THX!! So appreciative! Steph