Starting in version 4.0 on iOS and macOS, all users have access to Dark Mode in Day One on iOS devices.
To enable, go to Day One > Settings > Appearance > Dark Mode. Choose to enable on a scheduled basis or Always Dark.
The Map is not displayed at the bottom of entries in Dark Mode at this time but will be available on iOS 13 in Fall 2019.
Starting in version 2.9 and macOS 10.14 Mojave, Dark Mode can be enabled. This is done in the System Preferences > General. Choose the Dark appearance at the top. Day One will then be in Dark Mode.