I used code here. I have modified it to formless code already.
<!-- SiteSearch Google -->
<table border="0" bgcolor="#ffffff">
<tr><td nowrap="nowrap" valign="top" align="left" height="32">
<a href="http://www.google.com/">
<img src="http://www.google.com/logos/Logo_25wht.gif" border="0" alt="Google" align="middle"></img></a>
</td>
<td nowrap="nowrap">
<input type="hidden" name="domains" value="coolcoolgame.com"></input>
<label for="sbi" style="display: none">輸入您的搜尋字詞</label>
<input type="text" name="q" size="31" maxlength="255" value="" id="sbi"></input>
<label for="sbb" style="display: none">提交搜尋表單</label>
<input type="submit" name="sa" value="搜尋" id="sbb" onclick="this.form.action='http://www.google.com/custom';this.form.target='_top';this.form.method='GET';this.form.submit();" ></input>
</td></tr>
<tr>
<td> </td>
<td nowrap="nowrap">
<table>
<tr>
<td>
<input type="radio" name="sitesearch" value="" checked id="ss0"></input>
<label for="ss0" title="搜尋網頁"><font size="-1" color="#000000">Web</font></label></td>
<td>
<input type="radio" name="sitesearch" value="coolcoolgame.com" id="ss1"></input>
<label for="ss1" title="搜尋 coolcoolgame.com"><font size="-1" color="#000000">coolcoolgame.com</font></label></td>
</tr>
</table>
<input type="hidden" name="client" value="pub-6988193309725860"></input>
<input type="hidden" name="forid" value="1"></input>
<input type="hidden" name="ie" value="UTF-8"></input>
<input type="hidden" name="oe" value="UTF-8"></input>
<input type="hidden" name="cof" value="GALT:#008000;GL:1;DIV:#336699;VLC:663399;AH:center;BGC:FFFFFF;LBGC:336699;ALC:0000FF;LC:0000FF;T:000000;GFNT:0000FF;GIMP:0000FF;FORID:1"></input>
<input type="hidden" name="hl" value="zh-TW"></input>
</td></tr></table>
<!-- SiteSearch Google -->
Here is the original code here.
<!-- SiteSearch Google -->
<form method="get" action="http://www.google.com.tw/custom" target="_top">
<table border="0" bgcolor="#ffffff">
<tr><td nowrap="nowrap" valign="top" align="left" height="32">
<a href="http://www.google.com/">
<img src="http://www.google.com/logos/Logo_25wht.gif" border="0" alt="Google" align="middle"></img></a>
</td>
<td nowrap="nowrap">
<input type="hidden" name="domains" value="coolcoolgame.com"></input>
<label for="sbi" style="display: none">輸入您的搜尋字詞</label>
<input type="text" name="q" size="31" maxlength="255" value="" id="sbi"></input>
<label for="sbb" style="display: none">提交搜尋表單</label>
<input type="submit" name="sa" value="搜尋" id="sbb"></input>
</td></tr>
<tr>
<td> </td>
<td nowrap="nowrap">
<table>
<tr>
<td>
<input type="radio" name="sitesearch" value="" checked id="ss0"></input>
<label for="ss0" title="搜尋網頁"><font size="-1" color="#000000">Web</font></label></td>
<td>
<input type="radio" name="sitesearch" value="coolcoolgame.com" id="ss1"></input>
<label for="ss1" title="搜尋 coolcoolgame.com"><font size="-1" color="#000000">coolcoolgame.com</font></label></td>
</tr>
</table>
<input type="hidden" name="client" value="pub-6988193309725860"></input>
<input type="hidden" name="forid" value="1"></input>
<input type="hidden" name="ie" value="UTF-8"></input>
<input type="hidden" name="oe" value="UTF-8"></input>
<input type="hidden" name="cof" value="GALT:#008000;GL:1;DIV:#336699;VLC:663399;AH:center;BGC:FFFFFF;LBGC:336699;ALC:0000FF;LC:0000FF;T:000000;GFNT:0000FF;GIMP:0000FF;FORID:1"></input>
<input type="hidden" name="hl" value="zh-TW"></input>
</td></tr></table>
</form>
<!-- SiteSearch Google -->
Here is the result I got form the browser's HTML source. Please compare the color words.
<!-- SiteSearch Google -->
<table border="0" bgcolor="#ffffff">
<tr><td nowrap="nowrap" valign="top" align="left" height="32">
<a href="http://www.google.com/">
<img src="http://www.google.com/logos/Logo_25wht.gif" border="0" alt="Google" align="middle"></img></a>
</td>
<td nowrap="nowrap">
<input type="hidden" name="domains" value="coolcoolgame.com"></input>
<label for="sbi" style="display: none">JzjMr</label>
<input type="text" name="q" size="31" maxlength="255" value="" id="sbi"></input>
<label for="sbb" style="display: none">jM</label>
<input type="submit" name="sa" value="jM" id="sbb" onclick="this.form.action='http://www.google.com/custom';this.form.target='_top';this.form.method='GET';this.form.submit();" ></input>
</td></tr>
<tr>
<td> </td>
<td nowrap="nowrap">
<table>
<tr>
<td>
<input type="radio" name="sitesearch" value="" checked id="ss0"></input>
<label for="ss0" title="jM"><font size="-1" color="#000000">Web</font></label></td>
<td>
<input type="radio" name="sitesearch" value="coolcoolgame.com" id="ss1"></input>
<label for="ss1" title="jM coolcoolgame.com"><font size="-1" color="#000000">coolcoolgame.com</font></label></td>
</tr>
</table>
<input type="hidden" name="client" value="pub-6988193309725860"></input>
<input type="hidden" name="forid" value="1"></input>
<input type="hidden" name="ie" value="UTF-8"></input>
<input type="hidden" name="oe" value="UTF-8"></input>
<input type="hidden" name="cof" value="GALT:#008000;GL:1;DIV:#336699;VLC:663399;AH:center;BGC:FFFFFF;LBGC:336699;ALC:0000FF;LC:0000FF;T:000000;GFNT:0000FF;GIMP:0000FF;FORID:1"></input>
<input type="hidden" name="hl" value="zh-TW"></input>
</td></tr></table>
<!-- SiteSearch Google -->
And there are another issue about the search result. I post it in the other post here.
http://www.dotnetnuke.com/Community/ForumsDotNetNuke/tabid/795/forumid/108/threadid/110698/scope/posts/Default.aspx
Thanks for your help~~