How can I make a custom tab of my “fan” page viewable only by a set group of people?
You can limit your page posts by language and countries.
click on public
choose the second option.
select country or language.
What ha14 mentioned in his comment works only on Fb profile. These settings do not work for Fb page.
You can't make a Fb page visible to just a set of people. At the max, you can put age restrictions and country restrictions on people who can see the page. To do this, go to your page and click on "Edit Page" on top right. "Manage Permission" page will open up. Here you can specify the age and country restrictions.
There is also a work-around for your case. If you have a small set of people whom you want to make the page visible, make all of them admins (Open your page->Click on "Edit Page"-> Go to "Manage Admins"). Now go back to "Manage Permissions" tab and check the box that says "Only admins can see this page".
However, I'll not recommend this because of security reasons. One admin can remove other admin. It is like giving keys of your house to your friend. Give it to them only if you are sure they won't lock you out.
Follow this procedure
Facebook privacy settings