The Tennessee militia law in force in 1861 dated back to 1836 but this is it.
Generals and general staff: of the same grade as in the United States army
Light Infantry: long blue hunting shirts, blue pantaloons, round black hat and red plumes.
Riflemen: long black hunting shirts, black pantaloons, hats as infantry, and white plumes.
Cavalry Each regiment of cavalry may choose the quality of the uniforms for their officers and privates and they are authorized to use domestic manufactures for the same: Provided, nerveless, that the coats and pantaloons of each officer and private, of each regiment, shall be of deep blue color.
The companies called up at the start of the war and in mid 1861 often wore uniforms based on the above regulation. Most men who joined in 1861 had no uniforms what so ever.
It does not appear that Tennessee adopted any new militia uniform regulations during the war.
Early in the war many local ladies societies often supplied the uniforms for the Tennessee troops in service. The Military and Financial Board was established to replace the uniforms for Tennessee troops on duty (gray frock coats). I believe the Confederacy took over this task in 1863. If The Military and Financial Board did supply any uniforms to Local Defense units being called up for local service during an emergency, then they probably would have issued them uniforms in storage at the depot meant for troops in the field. This would possibly be what is some times called the Tennessee pattern frock coat. These came in 9 button patterns and 7 button patterns.
I have not found any additional information, however I would predict that that The Local Defense companies would have worn civilian clothing with or without added military distinctions. Tennessee was having difficulties supplying her troops in the field and it would be doubtful if the State provided any uniforms to the Local Home Guard units. .Officers who were often a bit wealthier may have purchased some type of uniform.
I really am not an expert on Tennessee uniforms and can not help you very much. If you are interested in more information on the Tennessee pattern frock coat let me know.