I know this type of question is a pain, but what ethnicity do these children most look like?

I agree with the others who said Italy or southern europe. The cap the boy is wearing just says italian to me. The children got dark hair and what appears to be an olive skin tone, but it's hard to tell because the picture is faded. They appear to have deep set eyes, with dominent eyebrows. The one thing I did notice about their clothing is that the two on the donkey are wearing lightweight jackets, which means it was a bit cold where ever the picture was taken. What we don't know about the picture though, is wether the location where the picture was taken is acually the place of the children's origins or not, if it is, then their clothes, the background, and the donkey, become more important clues, if it isn't, then those factors hold less weight.