Here's one I came up with today, and I think it's a useful term of art:
"Doll collector" -- slang/jargon for a parent who wants a child who will never change, and never cease to be "innocent" as far as the parent knows.
This is related to what I've called, variously, "parental amnesia syndrome", or "My Little Johnny syndrome". It's addressed to the kind of parent who would say, with no irony at all, "Hey, I might've done drugs in junior high, or had sex in junior high... but My Little Johnny would never even think of doing things like that!"
Such people don't really want kids. They want dolls.
Or, as I heard Jocelyn Elders put it recently, "We've got this idea that ignorance equals innocence. Not so."