he minimum level required is usually hard-coaded into the plugin.

Open the main file of the plugin you want to change access rights for and search for ‘manage_options’. Chances are it will be in a function called either add_options_page(), add_submenu_page() or add_menu_page(). This basically means that the link to access the plugin will not be displayed to users who cannot ‘manage_options’.

To allow Editors to access the plugin, change all occurances of ‘manage_options’ to ‘edit_pages’.
To allow Authors to access the plugin, change to ‘publish_posts’.
To allow Contributors to access the plugin, change to ‘edit_posts’.
To allow Subscribers to access the plugin, change to ‘read’.

Note though, that any change will be wiped out when you update the plugin in the future.