I went to:
PythonistaAppTemplate/Assets.xcassets/AppIcon.appiconset

I replaced the files:
Icon_120.png Icon_152.png Icon_180.png Icon_40.png Icon_58b.png Icon_80.png Icon_87.png
Icon_120b.png Icon_167.png Icon_29.png Icon_58.png Icon_76.png Icon_80b.png

With my own icon.
When I compiled, I got a black icon.

On iPhone 6s, I traced the icon: Icon_120.png to be the problem for getting a black icon on the "desktop" on the iPhone.

I somewhere read, that transparency is not allowed for icons?

By opening the icon in GIMP, Image -> Flatten image
and do an export to PNG, the "Black icon" problem was solved.

Hope this helps someone else. ;)