Is there a word, similar to idiolect or sociolect that means "language spoken within a family"? I thought it might be "familiolect" but that gets a suspiciously low number of google hits, non of them from reputable linguistics sites.

Anybody know of an accepted term for this withi linguistics?

Perhaps an ecolect (link) from Greek oikos 'house'.

I put the concept into Onelook's reverse dictionary, and the only reasonable word that came up was "vernacular," which obviously isn't what you mean. I really wish there were a better reverse dictionary. In this day and age of Internet capabilities, I am surprised there isn't, but I've not found one.

Writer's Digest Flip Dictionary (Hard cover) Don't know if it's still in print.

David Crystal on DCBlog says the word is familect.