Country music is not really my forte, but I do know a good few extremely sappy songs.
Here's a short list off the top my head. I hope it helps

Songbird - Fleetwood Mac
Lost - Anouk
Always - Bon Jovi
Lady - Styx
Now onto my "Top 30 playlist"
1. Can't Take My Eyes Off Of You - Frankie Vallie
2. July july! - The Decemberists
3. Keep The Car Running - Arcade Fire
4. Anybody Seen My Baby - Rolling Stones
5. Kate - Bend Folds Five
6. Caring is Creepy - The Shins
7. Girls and Boys - Blur
8. Wolf Like Me - Tv On The Radio
9. Juicebox - The Strokes
10. Wishing On A Star - Rose Royce
11. Rock The Casbah - The Clash
12. We Used To Be Friends - The Dandy Warhols
13. American Baby - Dave Matthews Band
14. Dig - Incubus
15. Dreaming With A Broken Heart - John Mayer
16. Stay - Lisa Loeb
17. Phantom Limb - The Shins
18. Supreme People - Blackalicious
19. Time Of The Season - The Zombies
20. The Garden - Mirah
21. Oh Valencia! - The Demberists
22. Party People - Nelly ft. Fergie (serious guilty pleasure)
23. A Lack Of Color - Death Cab
24. Hump De Bump - RHCP
25. Happiness is a Warm Gun - The Beatles
26. Miss You - Rolling Stones
27. Tits On The Radio - Scissor Sisters
28. Apologize - One Republic
29. Gus: The Polar Bear From Central Park - The Tragically Hip
30. Helicopter - Bloc Party
I love this thread, so good for bored people

Slow dancing in a burning room...