Google Sites does not offer customisation to the content colour background of individual pages on your site, so, here is a quirky work around for you...
Go to your chosen page, ready for it's makeover! Click in the content area > Click on edit > html > copy and paste the code below into the html, make sure it's the very first line > remember to save your changes!
<div style="background-color:#C0C0C0; padding:3px;">
For a range of colours look at the wicked wiki link below ... be sure to use the hex codes ... Simply replace my chosen colour's digits C0C0C0 with your six digit hex code, make sure you leave the # and the rest of the code in tact.
Please do comment in here a link to the pages you have made over with this trick! I look forward to seeing them!