I find that when trying to analyze obscure or weird occurances that using inverse logic can help greatly.
In a nutshell (to quote Spock the Vulcan) "when you remove the impossible, all that is left must be true".
So, what are Black Eyed Children?
They are not any part of any known race or culture.
They do not have a natural human appearance, i.e. jet black eyes, odd clothing.
They generate an aura that produces unease (to terror) is those that observe them.
They behave in an inexplicable and threatening manner.
So, we have an idea of what they are not. They are not "human".
What other malevolent sentient creatures that are capable of taking humanoid form exist?
The list is real short --> demons.
What about a couple of Mormons???