First off, there is no generic "manage users" ability. There are several individual abilities under that rubric. See http://codex.wordpress.org/Roles_and_Capabilities
Anyway, you have a couple options.
- You can add certain capabilities to existing users or
- you can create a new custom role with the capabilities you need.
If a brand new role is needed, one can be created using add_role() and add_cap():
$role = add_role('foo_doer', 'Foo Doer');
If you want to manipulate a user specifically:
// get user by user ID
$user = new WP_User( $id );
// or get user by username
$user = new WP_User( null, $name )
// add $cap capability to this role object
$role_object->add_cap( $capability_name );
That's the basics. A full and elegant rundown is here: http://www.garyc40.com/2010/04/ultimate-guide-to-roles-and-capabilities/