How to have multiple Google Custom Search field on the same page

I'm trying to have multiple search field on the same page with Google Custom Search (GCS) like this :

<script>
  (function() {
    var cx = 'user_id:field_id1';
    var gcse = document.createElement('script');
    gcse.type = 'text/javascript';
    gcse.async = true;
    gcse.src = (document.location.protocol == 'https:' ? 'https:' : 'http:') +
        '//www.google.com/cse/cse.js?cx=' + cx;
    var s = document.getElementsByTagName('script')[0];
    s.parentNode.insertBefore(gcse, s);
  })();
</script>

<gcse:search></gcse:search>

<script>
  (function() {
    var cx = 'user_id:field_id2';
    var gcse = document.createElement('script');
    gcse.type = 'text/javascript';
    gcse.async = true;
    gcse.src = (document.location.protocol == 'https:' ? 'https:' : 'http:') +
        '//www.google.com/cse/cse.js?cx=' + cx;
    var s = document.getElementsByTagName('script')[0];
    s.parentNode.insertBefore(gcse, s);
  })();
</script>

<gcse:search></gcse:search>

Unfortunatly, It does not work. The search is made with the same cx for every field. When It do the ajax request on this address : https://www.googleapis.com/customsearch/v1element... there is this value : &cx=user_id:field_id1 and the value is the same for both fields.

What is the solution?

I already seen this question : Multiple Google CSE (Custom Search Engine) Boxes on Same Page, but it seems to be on another version.

Solution

Try using iFrames:

index.html

<html>
    <head>
        <title></title>
        <style type="text/css">
            /* Layout Style */
        </style>
    </head>
    <body>
        <iframe src="gcse1.html"></iframe>
        <iframe src="gcse2.html"></iframe>
    </body>
</html>

gcse1.html

<html>
    <head>
        <title></title>
    </head>
    <body>
        <script>
            (function() {
                var cx = 'user_id:field_id1';
                var gcse = document.createElement('script');
                gcse.type = 'text/javascript';
                gcse.async = true;
                gcse.src = (document.location.protocol == 'https:' ? 'https:' : 'http:') +
                    '//www.google.com/cse/cse.js?cx=' + cx;
                var s = document.getElementsByTagName('script')[0];
                s.parentNode.insertBefore(gcse, s);
            })();
        </script>
        <gcse:search></gcse:search>
    </body>
</html>

gcse2.html

<html>
    <head>
        <title></title>
    </head>
    <body>
        <script>
            (function() {
                var cx = 'user_id:field_id2';
                var gcse = document.createElement('script');
                gcse.type = 'text/javascript';
                gcse.async = true;
                gcse.src = (document.location.protocol == 'https:' ? 'https:' : 'http:') +
                    '//www.google.com/cse/cse.js?cx=' + cx;
                var s = document.getElementsByTagName('script')[0];
                s.parentNode.insertBefore(gcse, s);
            })();
        </script>
        <gcse:search></gcse:search>
    </body>
</html>