To determine the total number of black-colored sulphides among the given compounds, we will need to identify the color properties of the sulphides of lead (PbS), copper (CuS), mercury (HgS), manganese (MnS), silver (Ag₂S), nickel (NiS), cobalt (CoS), bismuth (Bi₂S₃), and tin (SnS₂). The colors of these sulphides are characteristic of their chemical composition.

PbS (Lead Sulphide): Lead Sulphide appears as a dark, metallic gray to black color. It is commonly known as galena in its mineral form.
CuS (Copper Sulphide): Copper Sulphide can be found in various shades, including a dark, nearly black color, known as covellite.
HgS (Mercury Sulphide): Mercury Sulphide exists in two forms - cinnabar (red) and metacinnabar (black). So, HgS in its metacinnabar form is black.
MnS (Manganese Sulphide): Manganese Sulphide often appears in a green to pale pink color, but it is not typically black.
Ag₂S (Silver Sulphide): Silver Sulphide is black. It is commonly known for tarnishing silver into a black color.
NiS (Nickel Sulphide): Nickel Sulphide can vary in color, but the most common form is a dark bronze to black color.
CoS (Cobalt Sulphide): Cobalt Sulphide can exhibit a variety of colors, from pink to black depending on the specific conditions and forms. However, the most commonly encountered form, linnaeite (Co₃S₄), can appear gray to black.
Bi₂S₃ (Bismuth Sulphide): Bismuth Sulphide is characterized by a dark brown color, which can appear nearly black.
SnS₂ (Tin(IV) Sulphide): Tin(IV) Sulphide, or cassiterite, is usually yellow to brown, not black.

Based on the descriptions, the sulphides that are black are PbS, CuS, HgS (metacinnabar form), Ag₂S, NiS, and potentially CoS (though CoS can vary and might not always be classified as black, but we will count it here given its common dark forms). Thus, the total number of black-colored sulphides is 6 (including CoS). If we are strictly defining black without including the darkest variations of other colors, we would primarily count PbS, CuS, HgS in its metacinnabar form, Ag₂S, and NiS, with CoS being a conditional addition based on form.