Absolutely! Painting your own sink basin is a great way to save a little money and get the exact look you want. 

-First you'll want to prep the surface by sanding. A 100 grit sandpaper would work great!

-For the paint, we recommend Sherwin Williams Industrial Enamel. It's an oil-based paint, which is what you'll need to create a watertight surface. A quart of Industrial Enamel should be more than enough!
-Do not use a brush! We've found a foam roller works best!!