Trying to customise 2011 Child Theme Background Colour

Background-color:

body.custom-background {
        background-color: #0f0f0f; /* Color for the two borders */
}

#page {
    background: #0f0f0f; /* Color for the content/body part in the center */
}

#site-generator {
    background: #0f0f0f; /* Color for the footer part in the center */
}

You can also take it together into one snippet that changes the color of all three:

body.custom-background, #page, #site-generator { background: #0f0f0f; }

Your page background is kind of ‘split’ in two parts. Two borders at the left and right side and the center part.

This situation is the same in the footer. You can change the color of the middle section (like you did), but not the border color. The first part (body.custom-background) is about the border and applies to both the border besides the content and besides the footer. So if everything should be black, applying the above code is enough. You can put it in Customizer > Additional CSS.

I now chose for the color #0f0f0f, because that is the current background color. If you want pitch-black, choose #000000.

Let me know how it does!