Magento 1.9 – Add JS File to Module and Insert into Module Layout

First check if the layout handle is correct.
Add this line in the controller to see the layout handle

echo $this->getFullActionName();

I have a feeling it will print something like this adminhtml_module_sync_index. This is the layout handle you have to use in the layout file.
Also, just to be save, add a name and alias to the block from the content section.
Something like this:

    <adminhtml_module_sync_index><!--put here what you get from the echo in the controller -->
        <reference name="head">
            <action method="setTitle" translate="title">
                <title>Module</title>
            </action>
        </reference>
        <reference name="content">
            <block type="module_sync/adminhtml_index" template="sync/index.phtml" as="index" name="index" />
        </reference>
    </adminhtml_module_sync_index>

The tag should be used if you create a module that impacts an other one. and your declaration file (app/etc/modules/Namespace_Module.xml) this:

<?xml version="1.0"?>
<config>
    <modules>
        <MyCompany_MyModule>
            <active>true</active>
            <codePool>community</codePool>
            <depends>
                <Mage_Sales />
            </depends>
        </MyCompany_MyModule>
    </modules>
</config>

so finally your xml will look like

EDIT

to use adminhtml custom theme

if you are using like this in frontend design\frontend\default\yourtheme

then in admin you can also use design\adminhtml\default\yourtheme

you it should work like your custom in admin area please don't put in base else when you going to upgrade your magento version it may create issue.

i hope it will work for you.