True - Spandau Ballet
One On One - Hall & Oates
Feel Flows - The Beach Boys
Dreams - The Cranberries
Clocks - Coldplay
Medication (acoustic) - Garbage
We May Never Pass This Way Again - Seals & Croft
It wouldn't Have Made Any Difference - Todd Rundgren or Alison Krauss versions
Advice For The Young At Heart - Tears For Fears
Freedom - The Pointer Sisters
Just A Song Before I Go - Crosby, Stills & Nash
Time After Time - Cyndi Lauper
Fumbling Towards Ecstasy - Sarah McLachlan
Sparkling In The Sand - Tower Of Power
Song For Juli - Jesse Colin Young
Long Ago And Faraway - James Taylor
The Wind - Cat Stevens
Tables Turned - The Motels
I Go To Sleep - The Pretenders
Highway In The Wind - Arlo Guthrie
Sometimes In Winter - Blood, Sweat And Tears
Box Of Rain - Grateful Dead
For A Dancer - Emmylou Harris &Linda Ronstadt version or the original Jackson Browne.
Never Can Say Goodbye - Jackson 5
Summer Wind - Frank Sinatra
Wild Is The Wind - David Bowie version
Most Dionne Warwick songs
The Look Of Love - Diana Krall, Shirley Bassey, Diana Ross or, my favorite, the original Dusty Springfield version
What A Wonderful World - Tony Bennett & k.d. Lang duet.
The Closer I Get To You - Roberta Flack
Traces of the Western Slopes - Rickie Lee Jones
Soul To Squeeze - Red Hot Chili Peppers
The Beautiful Ones - Prince
Jericho - Joni Mitchell (Miles Of Aisles)
Hope this gets you off to a good start. Don't know what you mean by "meaningful", exactly. Lot of older stuff, but haven't been listening to much "mellow" new stuff (which is almost always "new & improved" old stuff).