Yeah, the whole fanny thing can be a problem!
But that's what I called it when I was a kid, I think. I'm pretty sure I knew it was a vagina but preferred calling it a fanny. Now I normally say vagina, or vajayjay or pussy if speaking to DH (err, won't be teaching the kids that one!).
My sister calls my niece's a mitzi - absolutely no idea where that came from.
I don't know what we'll call it, I think probably interchange vagina with another "pet" name so they know what it is and aren't too embarassed of that word. Then again most kids probably are embarassed about their private parts!
Penis will be willy, but again I'll call it penis too so they know what it is.