I suspect that a lot depends on the wood you are intending to dye, and what the carved item will be used for. If you use something like a mixture of iron water, red wine and oak galls you'll get a dark brown stain, if you use copper you'll get viridian green but it'll be toxic, so not suitable for a spoon. Ground madder roots mixed into an ointment type paste will stain a pale wood reddish colours, but will give darker plum shades on darker wood, and it's not toxic. There are lots of recipes like this, but as I wrote, they depend on materials and use. Stained carvings can look stunningly effective though
Cheers,
Toddy