Try mixing different amounts of instant coffee with clear aloe vera gel, like what you buy for sunburns. It will keep it from running unless that is the effect you are going for. The aloe will wash out leaving the dye/coffee/tea behind. I would play with some scraps using this, just coffee or tea and at different strengths and see which appeals to you the most.
Dry fabric will give you one look, and damp another :D:D:D