To remove coffee stain from slate kitchen counters, follow these steps:

1. Blot the stained area with a clean, damp cloth or paper towel.
2. Mix a solution of equal parts water and white vinegar.
3. Dip a soft-bristled brush or sponge into the solution and scrub the stained area.
4. Rinse the area with clean water.
5. Dry the area with a clean, dry cloth.

If the stain persists, repeat the process or try using a commercial slate cleaner. Avoid using harsh chemicals or abrasive sponges or scouring pads, as they can damage the slate surface.