The online Children's Songbook interactive music player allows you to transpose the key of the piece to suit the level of your student and the chord letters written in above the music guide them to know the order of chords even if they aren't reading notes fluently on the staff yet.
1. I begin with my version of "Fun to Do,"a song that is often sung by the children in the Church of Jesus Christ of Latter day Saints in primary. We sing "Singing with Chords is fun to do..." while accompanying with I and V root chords in C Major. Young children can just play the "chord shells" (outer 2 notes of the chord) if playing the middle note is too difficult.
2. Next I teach by rote the G 1st inversion chord which eliminates the need to hop the hand around as they can instead just slide (or melt) their 3rd and 5th fingers down one note to play the G chord.
3. Once they can easily transition between the I and V chords, they apply that knowledge to songs in other keys.
Following is a list from the Children's Songbook of the Church of Jesus Christ of Latter Day Saints with only I and V chords.
Fun to Do Lyrics "Playing with Chords is Fun to Do!"
Springtime is Coming
Wise Man and the Foolish Man 281
It's Autumn Time 246
Here We are Together 261
Healthy Wealthy and Wise 280
Rain is Falling 241
Hello Friends 254
In the Leafy Treetops 240
Our Door is Always Open 254