I am aware that you all know the primary definition of "binky"
1.(informal, childish) A stuffed animal, blanket, or toy that a small child is more attached to than any other, and often sleeps with.
2.(US, informal, childish) A baby's pacifier. See Pacifier. In the U.S. (Reg. 0334946) and a number of other countries, BINKY is a brand of pacifiers, owned by Playtex Products, Inc.
But there is another less common meaning and it's up to you to provide me with what you believe it is. No checking for the actual definition. I want your most creative notions of what the word could mean. Send me your ideas in a PM.
I'm no expert on babies but I've never heard of a binky, either as a child's sleeping companion or as a pacifier (what we'd call a dummy). I have heard of a favourite blanket being called a 'blankie', though.
There is one connection in which I have seen the word, and that is as a name so it won't fit the requirements of the game. It is, sadly, rather relevant as it is the name of Death's horse in the late great Terry Pratchett's Discworld books.
Build a man a fire and he's warm for a day. Set a man on fire and he's warm for the rest of his life.