Add a parallax image behind a page entry header in Genesis - pure css solution. (You'll need to style your image to be tall enough to match the webpage header, so it is behind the main page header on scroll)
Create a sidebar for a specific page with the Genesis Framework, without a new template file.
This allows you to use the built-in secondary sidebar as an alternate on one sidebar themes (you'll want to register a separate sidebar if you are using two sidebars in your theme layouts). This has a limited scope, I would recommend a plugin like Display Widgets if you are going to have a more complicated page-by-page application.