A synopsis from Basset Hull's book on Tasmania:
Perkins Bacon printed a lilac shade of 6d stamps in 1857, a superior impression but often seen faded to shades of grey, greenish or pale-brownish lilac.
In 1860 (Davies) and 1863 (Birchall) printed 6d stamps in slate or bluish-grey.
In 1865 the government printer issued 6d stamps in a bluish-grey shade then in 1867 and 1869 printed them in a red-lilac shade, which continued in use until 1875.
The shades found on perforated stamps are listed by Basset Hull as:
Perforated by Walch and Sons, 1864-1870
Lilac, Reddish-Lilac, Slate, Purple (shades)
Reddish-Lilac, Grey-lilac, Slate, Violet (March 1875 Bright violet), Violet with fugitive ink (Jan 1881 and Mar 1882) (shades of each colour)
Perforated unofficially in Launceston (by Harris?) 1864
Perforated 12 and 13:
Reddish-Lilac, Grey-lilac, Lilac, Slate (shades)
Roughly punctured roulettes (gauge about 8) by Walch and Sons, 1864
Rough irregular pin perforation (about 10.5) by unknown, 1867-1868
Rough parallel oblique 'saw-like' perforation (between 11 and 13) by Postmaster at Deloraine, 1867-1869
Grey, Slate (shades)
The Stanley Gibbons Australia catalogue lists further details on the various shades and perforation combinations, including a rare serrated perf 19 at Hobart (not observed on the 6d by Basset Hull) in Slate-violet and a 4.5 roulette in Reddish-mauve.