I really don't care for his covers (Betcha By Golly Wow, Everyday is a Winding Road, I Can't Make You Love Me), but I can think of other people's songs that would suit him well.

Madonna - Dear Jessie/Candy Perfume Girl
Marianne Faithfull - Broken English
Destiny's Child - Bootylicious
Michael Jackson - In The Closet
Phil Collins - In The Air Tonight
Culture Club - Miss Me Blind
U2 - Mysterious Ways/Even Better Than The Real Thing
Right Said Fred - I'm Too Sexy
Warrant - Cherry Pie
Maxwell - Cococure
Duran Duran - Notorious
Nine Inch Nails - Closer/Hurt

Billy Idol's - Flesh For Fantasy
George Micheal's - Fast Love (love to hear him work that break)
Maxwell's - Temporairy Night