We tried the dip dye thing about 12mths ago. Complete with bleaching.
It was fiddly, messy and my skills were sucky. So the results were not so great. The kids loved it though and had nagged me since to redo it.
There are a number of hair products around for temporary colouring. But they are a bit pricey for some fun in kid’s hair and there aren’t too many colours.
I recently discovered you can use chalk pastels for a similar effect. It is non toxic and cheap. They use it in cake decorating, so why not hair! I picked up a box super cheap on eBay, $16 for 64 colours.
It was really easy to apply. Can get a little messy, so I would suggest doing it outside. And maybe avoid helper dogs that are white.
You just wet the sections of hair you want to colour, and rub the chalk on until till its covered. Once you have done all the hair and it has air-dried, use a straightener to lock in the colour. It will last just a couple of washes, so nothing permanent.