How about adapting singing games? "Button you must wander" could use a little flower or leaf instead of a button.
Rarely does anyone, adult or child, these days know what a "paw paw" is, but I used the song my mother taught me in my teaching days; "Way out yonder in the Paw Paw patch." The younger children loved to act this one out.
I always enjoy teaching kids (of all ages) how to make Musical Instruments out of gourds: Shakers & rattles, beaded rattles. This is one of the easiest projects, and they can be easily painted, & yarn of various colors wrapped around the "handle" part.
   Seed pods from trees: I have some dried seed pods about 6 inches long in my "bag of tricks" for storytelling & performances with kids. They are wonderful lightweight shakers or rattles which can be held by little ones or the very elderly or folks who cannot manipulate well with their hands, & when shaken lightly make a quieter rattle.
   I also have a pair of sticks @ 6-10 inches long which I picked up off the ground under a tree outside the Music Dept. where I went to college. I have found plenty of others over the years. It's interesting to see the differences in the wood.
   There is a patch of bamboo-like reeds in my back yard which comes up every year. After it dries in the fall, I brought some in at the request of a young guitar student & he & his elderly neighbor experimented with making flutes, using some of my flutes/whistles from various parts of the globe. We found that after alot of practice, one can come up with a workable vertical flute. If you don't mind not-quite-accurate tuning. It's still fun to play, but the reeds are not as thick & hard as bamboo.
   Try clicking on the link Mudcat for kids or kidstuff for instructions for making instruments. One can use a dried large gourd cut down the middle longways to make a uke/mando-like stringed instrument such as a "canjo". After all, before the factories, people made instruments out of what they had.
We don't need no stinking store bought rhythm instruments & such!
   Good luck!