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To paint over stainless steel you'll need an oil based paint. You can use a brush, roller, or spray can as long as the quality of the oil based paint it good.
Taking a look at this webpage would probably be most helpful to you. Besides the paint type there are many other factors to consider when painting stainless steel, such as prepartation:
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Good evening (ss.......) You didn't indicate what SS you needed to paint but I can give you a personal experience. A couple of years ago on a remodel project we were confronted with an almost brand new range with a stainless steel front. We needed a high gloss black to go with the rest of the kitchen decor. A window installer that made a mistake by installing aluminum storm windows rather than white ones gave us the tip. I went to a local auto body supply store and purchased a can of metal etching spray. After masking off appropriate areas we sprayed on the metal etching paint. Being quite careful of course to not create any runs. Once dried we simply re sprayed with a high gloss black enamel. Any color would have worked. Results were fantastic.