I found a list of harmonica songs with tabs for you harp players. The guy at http://www.wildflowerharmonica.com/tabs/ (no affiliation) is apparently an instructor, so these must be "do-able." I'm sure there are many more out there.

B
B52s, The – Rock Lobster – 4th Position Scale Lesson
Beatles, The – Day Tripper – Cross Harp Lesson
Beatles, The – Here, There, and Everywhere – Harp Switching Lesson
Beatles, The – Let It Be – Middle / High Scale Lesson
Beatles, The – Love Me Do – Cross Harp & Breath Pattern Lesson

C
Christmas – Deck the Halls
Christmas – Jingle Bells
Christmas – Joy to the World
Christmas – O Christmas Tree
Christmas – Silent Night

F
Foster, Stephen – Camptown Races
Foster, Stephen – O Susanna
Foster, Stephen – O Susanna (cross harp version)

I
Irish – Connaughtman’s Rambles, The
Irish – Danny Boy
Irish – Harvest Home Hornpipe
Irish – Kesh Jig
Irish – Ms McLeod’s Reel
Irish – Parting Glass, The
Irish – Star of the County Down

K
Kids – Bingo
Kids – Do Re Mi
Kids – Frere Jacques (Are You Sleeping?)
Kids – Happy Birthday
Kids – London Bridge
Kids – Mary Had a Little Lamb
Kids – Pop Goes the Weasel
Kids – Row Row Row Your Boat
Kids – Twinkle Twinkle Little Star
Kids – You Are My Sunshine

L
Loops, Jeremy – My Shoes – Beatbox Lesson

N
National Anthem – The Star-Spangled Banner

P
Pitbull, feat Kesha – Timber – Articulation Lesson & Song History

S
Scales – The Blues Scale (Cross Harp)
Scales – The Major Scale (Straight Harp)
Scales – Minor Scales
Scales – Pentatonic Scales

T
Traditional – Amazing Grace
Traditional – Big Rock Candy Mountain
Traditional – Dueling Banjos
Traditional – Good Night Ladies
Traditional – Happy Birthday
Traditional – Reveille
Traditional – Shenandoah
Traditional – Taps
Traditional – What Shall We Do With a Drunken Sailor?
Traditional – When the Saints Go Marching In
Traditional – You Are My Sunshine
Twain, Shania – Nobody Needs to Know – Ear Training & Cross Harp Lesson