How to add a second custom menu in my sidebar when theme only supports one?

Search for the code give here in your themes functions.php file. and register second nave menu as show here.

register_nav_menus( array(
    'primary-nav' => "Primary Menu", // file may have this with different name
    'sidebar-nav' => "Sidebar Menu"   //add this line
) );

Use custom menu widget to show it up in sidebar. OR
If you want to edit the theme template, then put following code where you want the second menu to appear put follwoing code

<?php
wp_nav_menu( array(
    'theme_location' => 'sidebar-nav'
) );
?>

Now you can got to Menu Appearance Screen to assign items to it.