Cony's house is Cony's home mentioned in LINE TOWN.
This peach-coloured house with two "rabbit ears" is located on an island of the lake, which has a bridge with pink fences to connect. There are a lot of flowers and grass surrounding it, and there is a path at the middle. Its "mischievous grin" is actually made by two automatic doors, and its "eyes", which have purple and yellow shades, are the windows.
Cony's house is the only house which has automatic doors.