A "ring" has developed in our bathroom sink,... like a bathtub ring

What is the sink made out of?

Use a pumice stone.

ajax usually works, just be careful it doesn't scratch your finish

ditto! Pummie stick is the best. 2.99 at Home Depot or Lowe’s. Amazing.

white vinegar should do it x

try using, the cleaner for glass top stoves,, never ever ever use an abrasive type sponge on anything in the bathroom, it will mar the finish. Toilet bowl cleaner gel type let sit overnite. will help. Also check the drain it must be draining too slowly

Try. Bar keepers Friend

If the sink is not some unusual material, then I would try a paste of baking soda and bleach, spott scrubbing with something that has more bristles than sponges, like an old toothbrush, or fingernail brush. Leave sit for a while before rinsing off.