Since I don't know your audience I can't give you any cant miss songs, but my wife's taste in music is a complete 180 from mine, and she really likes when I play "Please Be With Me" by Cowboy. Great if the other member of your duo can play the Duane Allman slide part.
A few others that she doesn't mind me playing are
Hurt- Johnny Cash
The Flame- Cheap Trick
Wish You Were Here- Pink Floyd
Then again, maybe she just likes these because she doesn't have to hear my amp.
Ventura Highway - America
Lyin' Eyes - Eagles
South City Midnight Lady - Doobie Bros
Come Monday - Jimmy Buffett
Leavin' On A Jet Plain - John Denver
Southern Cross - CSN&Y
Get Together - Jessy Colin Young & Youngbloods
Easy To Be Hard - Three Dog Night
Sailin' - Christopher Cross
Imagine - Chet Atkins version
Here's a few more:
Johnny Winter - Cheap Tequila, Ain't nothin' to me
Simon and Garfunkel - Sounds of Silence, A Hazy Shade of winter
Badfinger - Baby Blue
Moody Blues - The Story in Your Eyes
Rolling Stones - Wild Horses, As Tears Go By, Angie, You Can't Always Get What you Want, Love in Vain.
Creedence Clearwater - Midnight Special, Bad Moon Rising, Lodi.