Using Google Custom Search Engine with Google Sites is impossible, because script tags will be removed. The HTML source I tried to use:
<script src="http://www.gmodules.com/ig/ifr?url=http://www.google.com/coop/api/000162166689316991215/cse/whsntg5ttva/gadget&synd=open&w=320&h=75&title=Test+Search+Engine%3A+Google&border=%23ffffff%7C3px%2C1px+solid+%23999999&output=js"></script>
My Google Custom Search Engine page:
http://www.google.com/coop/cse?cx=000162166689316991215:whsntg5ttva