In Google Sites you can not use YouTube Custom Player, because Google Sites removes object tags. This is the HTML source I tried to use:
<object width="416" height="337"><param name="movie" value="http://www.youtube.com/cp/vjVQa1PpcFOEuUF1goZTKrIR7vIZ9O1uIk75sxWnQ6w="></param><embed src="http://www.youtube.com/cp/vjVQa1PpcFOEuUF1goZTKrIR7vIZ9O1uIk75sxWnQ6w=" type="application/x-shockwave-flash" width="416" height="337"></embed></object>
More info about YouTube Custom Player:
http://help.youtube.com/support/youtube/bin/answer.py?answer=71796&topic=12140
http://help.youtube.com/support/youtube/bin/answer.py?answer=71798&ctx=sibling&topic=12140