I don't really know what kind of songs work well for Karaoke
If you can do Sweet Caroline, try some other Neil Diamond songs. I like Solitary Man and He Ain't Heavy.
It's a different vocal range, but I think some Meat Loaf songs would be good in a lower pitch.
Bill Withers - Ain't No Sunshine
If I were A Carpenter - Take your pick of singers
George Gershwin - Summertime
Usually sung by women by I think it would be good in a lower register. Probably hard to pull off, but would be really cool if you can do it.
Bob Seger - Turn The Page, Against The Wind
James Taylor - Fire and Rain
Johnny Cash - Hurt
One of my favorite songs to cover.