What sort of drone are you looking for, and what sort of programmable?
This tiny $20 quad has a hacked, open firmware: https://hackaday.com/2016/01/07/open-source-firmware-for-a-m...
This tiny $20 quad has a hacked, open firmware: https://hackaday.com/2016/01/07/open-source-firmware-for-a-m...
... and now I learn that I can hack the firmware! so for an "affordable programmable drone suitable for children", I think that's the best answer (it's just $14 on banggood). Buy spare batteries though, and maybe with budget < $100, buy two of them :)