Unfortunately, page color is document-specific so you can’t change it for different pages.  Perhaps the easiest way is for the particular page you want colored differently to include a header with a colored shape that fills the entire page.

Create the new page in its own section.  

On the next page click in the header area and unselect the option to Link to Previous header. 

Insert a rectangle sized to fill the page. 

Size it at exactly the same as your paper size.

Set the Wrap Text option to display the shape Behind Text.

Make sure that you create a new section break after this page and again unselect Link to Previous so that the shape doesn’t appear on subsequent pages.  Delete the shape from the header after you get to the next page.