Here's what I hope people do, keeping in mind that while I love Neil, I really only know the famous stuff:
David Cook: "Cracklin' Rose" or "Brother Love's Travelin' Salvation Show," rocker style
David Archuleta: please, PLEASE don't do one of the soulful ballads like "Hello Again," "I Am, I Said," or "Heartlight." How about "Forever in Blue Jeans"?*
Syesha: "You Don't Bring Me Flowers"
Michael Johns: "Sweet Caroline"
Brooke: "Song Sung Blue"
Jason Castro: "America" or "Shilo." Or "Red, Red Wine."
Carly Smithson: "Girl You'll Be a Woman Soon"
Kristy Lee: Honestly, I don't care, but for pure kitch value, how about "On the Robert E. Lee"?
*Looking through this list of Neil Diamond songs, I learned that in 1968, he recorded a tune called "The Pot Smoker's Song." I don't know it, but I think it would be hilarious if David A. sang that one! So not gonna happen.