So I'm going to take you back a couple decades to the Hap Palmer era. Hap Palmer earned a Master's degree in dance education in the early 80s, but was writing children's songs years before that, in the late 60s. The songs were written to enhance a number of developmental skills in young children. Below are five videos I found when conducting a youtube search, though you'll find he composed hundreds more.
The videos below can be used as is in session. But if you find these dated, I encourage you to let them inspire your own creativity! If you have any Hap Palmer songs of your own that you love, or any other ideas for that matter, please share!
Tap Your Sticks
Bean Bag Alphabet Rag
Let's All Clap Our Hands Together
The Mice Go Marching