Cheers.
I first tried bleaching before toning in sodium carbonate, using Magnani Portofino hot-press watercolour paper, but the bleaching made the print look faded and the paper stained horribly.
Then I tried a short toning (30 minutes) without bleaching on the other paper that I use which is a very cheap store-brand hot-press watercolour paper, and that turned out significantly better, with decent dark eggplant blacks and quite acceptable levels of staining. Unfortunately I can't really tell you much about the paper as it is just re-branded by a local art store chain, but it's 230 gsm and almost certainly not pure cotton or anything fancy. Here's a link:
Pad of 230g Wet Strength Mixed Media Cartridge Paper. Double sided - canvas finish/smooth finish. 30 Sheets Portrait Pad Wet Strength papers are recommended for printing, proofing and wet media techniques. They have the ability to absorb water without deteriorating. Suitable for acrylic, oil...
www.gordonharris.co.nz
I think the paper makes a huge difference to how bad the staining is, and I couldn't tell you what it is about this paper that works, maybe the sizing?
I use 6 tablespoons of cheap instant coffee powder dissolved in 500mL of boiling water, which is then added to 3L of cold water (I had quite a few prints to tone and a large tray). I pre-soaked the prints in water in the hopes that it might prevent the paper absorbing too much of the coffee, and then placed the wet prints face-down in the coffee and let them sit for 30 minutes before removing and washing.