This list was compiled by manson26 and TeeJay and may not be all inclusive.
Songs in green are ones you can obtain from CDs/iTunes from the respective artists.

Episode 1×01

1. Hallelujah, I’m Ready – Traditional Hymn, Public Domain
2. Big Band Dream – Jono Grant
3. It’s A Lovely Day Tomorrow – Charlotte Hegele
4. A Hundred Years From Today – Adaline

Episode 1×02

1. Mischievous Moon – Jill Barber
2. Daydreamin’ – Jill Barber
3. You’ll Never Know – Alex Pangman

Episode 1×03

1. Lonesome Valley – Charlotte Hegele
2. Red River Valley – Charlotte Hegele
3. Hey Cinderella – Berl Olswanger (classicsonline.com)
4. I’ll Never Be The Same – Billie Holiday with Teddy Wilson & His Orchestra

Episode 1×04

1. Run Away Train – Jim Codrington (charfin.com – Different Version)

Episode 1×05

1. Drum Boogie – Jono Grant
2. BB Blues – Jono Grant
3. Flowers of the Forest (Courtesy of Audio Network Canada)
4. I Wished On The Moon – Charlotte Hegele
5. Oh My My – Jill Barber

Episode 1×06

1. Be Careful What You Wish For – Charlotte Hegele
2. Ain’t Nobody’s Business If I Do – Adaline

Episode 2×01

1. Watch the Birdie – Anita O’Day
2. Boogie Woogie Bugle Boy – Jill Barber
3. Fast Talkin’ Man – Jill Barber
4. Take It Off Your Mind – Jill Barber
5. One More Time – Jill Barber
6. I’m Pulling Through – Billie Holiday & Her Orchestra

Episode 2×02

1. Tangerine – Royal Wood

Episode 2×03

1. Just As I Am – Choral Performance by New Life Covenant Centre Choir

Episode 2×04

1. Won’t You Come See Me – Brett Dier & Jodi Balfour
2. Glory, Glory – Choral Performance by New Life Covenant Centre Choir

Episode 2×06

1. Witham Jingle – Jono Grant & Michael MacLennan
2. I Don’t Want to Walk Without You – Charlotte Hegele

Episode 2×07

1. Mother’s Whistler – Jack Millman
   
2. Jono Grant – Jewel Box Jitterbug
3. Flow – Emma-Lee

Episode 2×08

1. Betcha Nickel – Tanika Charles
2. Jewel Box Jitterbug – Jono Grant
3. There Is a Balm in Gilead – Charlotte Hegele

Episode 2×09

1. Martini Moll – Heinz Kiessling
2. The Man I Need – Charlotte Hegele