this should do it. not sure if popup blockers will complain about the JavaScript window.open stuff (i don't use popup blockers, so please test this).
Code:
<script type="text/javascript">
function doSearch()
{
var frm = document.forms.search;
var q = escape( frm.q.value );
var site = frm.sitesearch.value;
var url = "http://www.google.com/search?q=" + q + "&sitesearch=" + site;
window.open( url );
}
</script>
<form name="search">
<input type="text" name="q" size="31" maxlength="155" value="" />
<input type="button" onclick="doSearch()" value="Search" />
<input type="hidden" name="sitesearch" value="mysite.com" />
</form>