How do you patch a rusted sink by the drain?
Answers:
Face it sweetie, you are going to have to replace the sink eventually. But, what you can do temporarily, at least, depends on whether or not there is any sizeable hole or leak. If there is no hole, you could clean up the rusted area as well as you can and mix up a good grade of liquid epoxy and coat the affected area with that. If you actually have a hole, you could use epoxy putty, which you knead into a soft mass and then squish up into the hole from underneath, smoothing out anything that squishes out above. You could also coat this with the liquid epoxy from above to seal it all up real well and this should last a long time. Just make sure your surfaces are clean and dry (get off all the soap scum) before you do this.
Other answers:
TRY GETTING A NEW DRAIN OR USE SOME SILACONE
TRY GETTING A NEW DRAIN OR USE SOME SILACONE
If its a ceramic sink, you can get a touch up paint for it at a dealership. Follow directions.
Sounds like a job for some fiberglass. You can buy inexpensive kits at most hardware stores.
you really have to replace the drain