I'm happy to help you recall a book or a guest from the show, but please note, I have no idea how to get an author and a book ON the show. I'm just a fan and am in no way connected with The Daily Show. If you're really keen, Zach Wahls (author of My Two Moms and guest on The Daily Show) has this to say ...
The way it works is that the publicist for my book (who works for Penguin, the publisher) pitched the Daily Show. TDS receives about 200 requests a day, so when my publicist, who's the woman with curly brown hair in the imgur album, called me to tell me that they were interested, I literally couldn't believe it. It's obviously an issue that Jon cares about quite a bit and it was a story in which he had considerable interest.