Google has just released a new feature for Google Sites. Now, you have the ability to use custom colors in the theme of your site. You can select a color from the color pallet or you can enter the hex code of the color. The website theme will change to the specified color you selected.
Just a side note, if you would like to pick a color using the hex code, I would recommend to download the FREE Chrome extension, ColorZilla from the Chrome Web store. This Chrome extension will allow you to pick a color from any webpage, then it will copy the hex code to the clipboard, which will allow you to paste it into the hex code area on the Google Site.
Here is a screen cast to demonstrate this new feature in Google Sites.
Here is the official blog post from Google.