I live for tie-dye! (Grateful Deadhead)
Hobbycraft (or insert your favourite craft store) has some
great blank-colour your own stuffed animals Then get yourself a tie dye kit These will all have squirt bottles in them, which will make your life really easy, rather than having to dip and dye and the colours will be really vibrant and are usually non-toxic. They don't need rinsed out- but you can wash the stuffed animal without them running fading
You can create neat patterns with rubber bands, clothespegs, binder pegs, pins, thumbtacks (to cover up areas), etc...