You can try using the epoxy kits,for that sold at Home Depot. Step by step instructions are in the kit. But you need to know it's temporary. Will peel if scratched. Painting sinks and tubs are a short lived endeavor.
Agree with Kelli. Although it seems to be a popular diy project at this point in time, the results depend greatly on the condition of the sink beforehand, proper preparation, and quality brand materials. Even so, the results can no where match the durability and longevity of a brand new sink.
How to Paint a Porcelain Tub, Sink or Toilet
Yes, the epoxy kits work great for bathroom sinks. :) My favorite is epoxy for this type of project is Stonecoat Countertops epoxy.
Thanks will try it