I know this thread is almost four years old, but it came up as the second result in my
Google search for Kate schema black background
The #1 result was
darK - A Kate Syntax Highlighting Theme - on KDE-Look.org. It is from 2007/2008, but has a reasonable rating and number of downloads [relatively speaking].
I manually installed
darK as per the Description's Installation instructions. I am using it on KDE4, so I had to substitute
.kde with
.kde4. I made it my
Default schema for Kate, and it appears to be working fine.
Hope this helps,
Daniel Shakhmundes