Stinky sinks generally result from bacteria growth inside the overflow bowl part of the sink. Look around the inside top of the sink bowl and you’ll see some overflow holes.
Bacteria can start growing inside the overflow bowl. The way to safely kill the bacteria is to get some hydrogen peroxide insde that sink bowl. Use 3% hydrogen peroxide (the kind you get at your local drug store).
The way we do is to put the hydrogen peroxide into a spray bottle and then spray, spray, spray through the overflow hole… making sure to spray in all directions into the bowl. Repeat as needed. This has worked well for us.
Another way would be to shove an old wash rag down the sink drain just far enough to stop up the place where the sink bowl overflow drains into the sink drain. Then take a funnel (will probably have to be a small size) and pour several bottles of hydrogen peroxide into the overflow hole. I could take a lot of hydrogen peroxide so spraying might be the simplest way.
However you do it, the trick is to introduce hydrogen peroxide into the sink overflow bowl. That will kill the bacteria and make your sink fresh as a daisy.