As Smiley says, there are epoxy paints out there to solve these problems.
We went with this product
https://www.amazon.com/Homax-720773-...231076&sr=8-34
We bought it at ACE Hardware several years ago for about $25.
More now. Comes in a brush on and spray on version. We chose the spray on so our cost was closer to $50 -- since it ruined my HVLP nozzle.
Most of the competing products come it kits designed for tub/shower/surround. So large quantities and large prices.
As with any epoxy, follow the directions to the letter. We've been happy with the result. You still have to clean, but it seems to resist staining better than the OEM.
SWMBO really wanted stainless, but the sink is an odd shape with one side longer and wider than the other. And I did not want to tackle cutting into the counter top corian. Good move, taking it out! This stuff ain't no Chanel #5.
With the 26oz can, we applied three coats to the kitchen sink, two coats to the vanity sink and assorted plastic flower pots. (Waste not, want not.)
Fair Winds and Following Seas