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:
GH WET STRENGTH CARTRIDGE 230G A3 PAD 30 SHT
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.