In a rental unit, I have a burned spot(about 2" in diameter )on the
formica kitchen countertop.

Short of replacing the entire kitchen countertop surface, are there
other solutions that have worked for the group's members?

If it's not too deep, you can try sanding it out, but the pattern is
probably just printed onto the laminate, and you'll sand right through
it.

My best solution is to put down another piece of laminate or tile.

Other option:
Use a router to remove a rectangular recess, then fill it with tile to
make a permanent trivet.

--
Steve Bell
New Life Home Improvement
Arlington, TX USA