Conny is an oni child that Tazuki keeps. He got his name from Tazuki who decided to join the words "ko" (child) and "oni" (demon) to form the name "Kooni" or, as his name is written, "Conny".
Conny is omnivorous and eats pretty much everything. He also has a bit of a temper and often tries to punch Tazuki despite being a harmless oni child.