Sure you can buy it in bulbous bottles from Michaels Craft store but in the spirit of the “make your own” trend why not try your hand at painting with egg yolks? Of course true tempera paint would require fresh eggs, a steady hand and proper pigments but a messy version can be made for children without the fuss. The emphasis is on MESS! This is a good recipe for thanksgiving week since the kitchen is a mess anyway and you may have a few spare egg yolks laying about.
Mix one yolk with one drop of food coloring for a sticky finger paint that will dry shiny. If you have some crumbly chalk left over from summer you could also try to mix the yolk with that. I must emphasise that this in no way properly represents the sort of medium that Giotto used to capture the subtleties of his Ognissanti Madonna. Like most projects for young children it is a sensory rich dip into creative expression that perhaps will open the way for a future interest in art. The idea is to introduce the concept of using a binder to paint with a pigment. If you want to know how to properly prepare egg tempera looking here would be a good place to start.
To preserve some semblance of sanity I highly recommend enacting the entire project on the floor atop a goodish spread of newspaper. Once the activity begins to reach the “unfun” point simply scoop up the whole mess and toss it in the trash or fireplace.