Tough to say what it is could be a number of things,
 
One time I had a custy who had a candle sitting on some slate and after time the oil from the candle left a circular oil stain that I removed with a poultice.
 
I sure some of the other guys will chime in some some thoughts.

--- On Tue, 12/9/08, Zev Guez <zev@stonerestorationplus.com> wrote:
From: Zev Guez <zev@stonerestorationplus.com>
Subject: [sccpartners] STAINS ON SLATE
To: "Restoration and Maintenance" <sccpartners@stoneandtilepros.com>
Date: Tuesday, December 9, 2008, 7:30 PM

Hi just got a call from a custy that she has a pc of slate in front of her fire place and it has stains on it. I asked her if it was oil and she said she does not know. Any ideas what it could be and any solutions (I THOUGHT IT COULD BE SMOKE BUT THE STAINS WERE CIRCULAR IN SHAPE)
  THANKS
--
Zev Guez
Stone Restoration Plus
(732) 309-3878
www.stonerestorationplus.com