The best solution is to add a widget area that all sites have access to use and then add a text widget.
How I handled this since I had one child theme being used was I added a functions.php file and copied a duplicate of the index.php from the parent theme file into the child theme folder.
My base steps were the same as in the solution @toscho posted: https://wordpress.stackexchange.com/a/76975/35677
This made a widgetable area across all the sites and this is what I wanted. An additional note though is to have my widget use the css and custom widgets of the theme i was using took a bit of manipulation. My theme included custom widgets ontop of the defaults with special formatting for the “title” of a widget a “line break” and then the widget “content”.
In my case I was able to get it to act like the themes native widgets with something like:
function welcome() {
register_sidebar( array(
'name' => 'Welcome Message',
'id' => 'welcome',
'before_widget' => '<div class="widget-top">',
'after_widget' => '</div>',
'before_title' => '<h4>',
'after_title' => '</h4><div class="stripe-line"></div></div><div class="widget-container">',
) );
}
add_action('widgets_init', 'welcome');
As you can see I had to do some custom tag ending to get it to work the same.