The dense media specific gravity is based on the amount of medium that is suspended in the water.  So the answer to your question is obviously 1.0 which is when you have no media added.  In effect this is how a jig works.  But in actual fact the density of the media will never reach 1.0 due to circulating fines and other factors. 

If you are actually asking what is the lowest realistic specific gravity you can use and control to, that depends on the type of media you are using and the physical characteristics of it.  Also the design of the media system to include screens, magnetic separators (assuming magnetite or ferro silicon).  A properly designed media system can usually control the media specific gravity to within 0.01+/- of a desired gravity.

Then you need to consider the characteristics of the coal.  Coal being made up of several different  coal type minerals (sometimes called macerals (probably showing my age with that)), and several types of waste the best separating gravity is determined by the cleaned coal specifications you want to achieve.

The one issue that does become an issue in a DMS cyclone plant is the stability of the medium and this relates to the differentials seen across the DMS cyclone, when operating at very low densities.

It should be noted that by the nature of how it performs a dense media cyclone will also have a variation in media gravity from the overflow and underflow.  The coarser the media particles the greater the media density variation, partly due to the classification action of the cyclone (and yes even dense media cyclones have a classification action - coarse to underflow, fines to overflow).