Please advise how to use alum to patinate sterling silver dark gray

I am having trouble colouring sterling silver for neck wires in jewellery-making, but right now to provide a good edge to support wire-knitted necklaces into which beads are knitted. Normally it is much easier to use silver uncoloured, or to use brass to match the design & colours of the other wire & beads. I have had some success with a few colours, using thorough pre-preparation & cleaning followed by sanding & painting several layers of top quality artist's permanent pens & layer; of clear lacquer.

But I would prefer a better way of changing the colour of silver to black, which is an important colour in this context, and have read that a good result can be achieved using 10-20% potassium alum in water. This solution is supposed to be better for me and the environment than liver of sulfur ⇦ on eBay or Amazon [affil link] . I did sanding, methylated spirits, detergent & good rinsing in water for preparation, & kept heating the alum in water to near boiling but got no results when testing.

I need to know this please to present a professional level of article to customers & would very much appreciate assistance

Simple and cheap gray patina for silver:

            1 heaping teaspoon kitchen salt
2 heaping teaspoons copper sulphate
2oo cc water Cold (or hot) immersion.Rinse well.