This Widget lists the sub-categories for a given category.
Installing is pretty easy takes only a minute or two.
Upload 'sub-category-widget' directory to your '/wp-content/plugins/' directory.
Activate the plugin through the 'Plugins' screen in WordPress.
On the 'Widgets' sub-menu of 'Appearance' you will find a new widget type called 'Sub Category'.
Add one or more of these to your themes widget display areas.
For each widget you add, decide what and how you'd like it to display.
Save your settings.