How do I remove black rings on a wood kitchen top formed by a tin can?
Oxalic acid, either in crystal form or as part of a pressure treated deck cleaner/brightner will chemically dissolve the stain.  If you use the crystals, use all normal precautions for acids (eye, hand, clothing).  You can sparingly apply with a small nylon artists brush.  Try 5 min increments (5 on, wipe off, 10 on, wipe off) until the stain starts to disappear.



Once stain disappears, neutralize wood with borax diluted in water or bicarbonate of soda in water.

Replace color with dyes or pigment stains.  I like Transtint for its ability to be blended and mixed with either water or alcohol. If you don't like the color direction, you can use bleach and start over.

Once happy with the color, seal it in with a dewaxed shellac.  Then top coat with your favorite polyurethane.  You may be able to blend the areas by shooting spray poly through a circular mask (5" hole in a 12x12 piece of cardboard, held 5-10 inches away from the floor) which will give you a graduated spray.  Practice first.