The user wants to find the total number of black coloured sulphides from the given list: $PbS$, $CuS$, $HgS$, $MnS$, $Ag_2S$, $NiS$, $CoS$, $Bi_2S_3$ and $SnS_2$.

This problem requires knowledge of the characteristic colours of common metal sulphides, a topic frequently covered in qualitative inorganic analysis.

Let's determine the colour of each sulphide one by one:

1. $PbS$ (Lead(II) sulphide): This is a well-known precipitate in qualitative analysis (Group II cations). It is black.

2. $CuS$ (Copper(II) sulphide): Also a Group II cation precipitate, it is black.

3. $HgS$ (Mercury(II) sulphide): When precipitated from a solution using $H_2S$, it forms a black solid (metacinnabar). Although a more stable red form (cinnabar) exists, the common precipitate is black.

4. $MnS$ (Manganese(II) sulphide): This is a Group IV cation precipitate. It has a characteristic buff or flesh-pink colour.

5. $Ag_2S$ (Silver(I) sulphide): This is the compound responsible for the tarnishing of silver. It is black.

6. $NiS$ (Nickel(II) sulphide): A Group IV cation precipitate, it is black.

7. $CoS$ (Cobalt(II) sulphide): Similar to $NiS$, it is a Group IV cation precipitate and is black.

8. $Bi_2S_3$ (Bismuth(III) sulphide): A Group II cation precipitate. It is described as dark brown or brownish-black. For the purpose of strict colour classification, it is not considered pure black.

9. $SnS_2$ (Tin(IV) sulphide): This is known as 'mosaic gold' and has a characteristic golden-yellow colour.

Now, let's list the sulphides and their colours:

• $PbS$: Black
• $CuS$: Black
• $HgS$: Black
• $MnS$: Buff/Pink (Not black)
• $Ag_2S$: Black
• $NiS$: Black
• $CoS$: Black
• $Bi_2S_3$: Dark Brown (Not black)
• $SnS_2$: Yellow (Not black)

Counting the sulphides that are explicitly black: $PbS$, $CuS$, $HgS$, $Ag_2S$, $NiS$, and $CoS$.

There are a total of 6 black coloured sulphides in the given list.