This solution gives you pretty much the same result as the code in this tutorial however you can add your image via the customizer rather than upload it to your child themes images folder.
Add the PHP code to the end of your child themes functions file. Thats it!
You can then upload your image via the customizer using the Custom Header Image setting as seen in the following screenshot :
You can also add a default in your child themes images folder named header.png.
Tested using the Genesis Sample child theme by StudioPress.
Here’s the code for logged in members :