How to use wp_register_script / wp_enqueue_script for multiple queries

If I understood you correctly you have to give your code a bit of refactoring and call wp_localize_script strategically.

Based on your code, I’d say you have two options.

1. You can call wp_localize_script once, add as many values as you want within $l10n array and create only one $object_name to be used within JS.
2. You can call wp_localize_script as many times as you need, but your $object_name needs to be unique for each time you call it.

Please pay attention to the code, especially the comments:

function register_scount_script() {
    // As a best practice use `get_stylesheet_directory_uri` instead of `get_template_directory_uri`, unless you really know what you are doing.
    wp_register_script( 'scount', get_stylesheet_directory_uri() . '/assets/js/us-states.js', array( 'jquery' ), '1.0.0', true );
}

/**
 * First method. You will call `wp_localize_script` once, add as many values as you want within $l10n array
 * and create only one $object_name to be used within JS.
 */
function localize_scount_script_first_method() {
    $args = array(
        'post_type'  => 'property',
        'fields'     => 'ids',
        'meta_query' => array(
            'relation' => 'AND',
            array(
                'key'   => 'state',
                'value' => 'NC'
            ),
            array(
                'key'     => 'available',
                'compare' => '=',
                'value'   => '1'
            )
        )
    );

    $results      = new WP_Query( $args );
    $nc_completed = count( $results->posts );

    // At this point, you can execute the query again and just change 'state' key value to 'SC', for instance.
    // Then you would have/create a new variable $sc_completed.

    /**
     * @param string $handle Script handle the data will be attached to.
     * @param string $object_name Name for the JavaScript object. Passed directly, so it should be qualified JS variable.
     * @param array $l10n The data itself. The data can be either a single or multi-dimensional array.
     */
    wp_localize_script(
        'scount',
        'completed',
        array(
            'nc_completed' => $nc_completed, // This value would be accessible in JS using var completed.nc_completed
//          'sc_completed' => $sc_completed // This value would be accessible in JS using var completed.sc_completed
        )
    );

    // Make sure you reset $wp_query global. If not you might have trouble somewhere else in your code.
    wp_reset_query();
}

/**
 * Second method. You will call `wp_localize_script` as many times as you need, but your $object_name needs to be unique
 * for each time you call it.
 */
function localize_scount_script_sec_method() {
    $args = array(
        'post_type'  => 'property',
        'fields'     => 'ids',
        'meta_query' => array(
            'relation' => 'AND',
            array(
                'key'   => 'state',
                'value' => 'NC'
            ),
            array(
                'key'     => 'available',
                'compare' => '=',
                'value'   => '1'
            )
        )
    );

    $results   = new WP_Query( $args );
    $completed = count( $results->posts );

    /**
     * @param string $handle Script handle the data will be attached to.
     * @param string $object_name Name for the JavaScript object. Passed directly, so it should be qualified JS variable.
     * @param array $l10n The data itself. The data can be either a single or multi-dimensional array.
     */
    wp_localize_script(
        'scount',
        'nc_completed', // Needs to be unique!
        array(
            'completed' => $completed, // This value would be accessible in JS using var nc_completed.completed
        )
    );

    // At this point you could perform a new query and localize again:
    $args = array(
        'post_type'  => 'property',
        'fields'     => 'ids',
        'meta_query' => array(
            'relation' => 'AND',
            array(
                'key'   => 'state',
                'value' => 'SC' // Changed to SC.
            ),
            array(
                'key'     => 'available',
                'compare' => '=',
                'value'   => '1'
            )
        )
    );

    $results   = new WP_Query( $args );
    $completed = count( $results->posts );

    /**
     * @param string $handle Script handle the data will be attached to.
     * @param string $object_name Name for the JavaScript object. Passed directly, so it should be qualified JS variable.
     * @param array $l10n The data itself. The data can be either a single or multi-dimensional array.
     */
    wp_localize_script(
        'scount',
        'sc_completed', // Needs to be unique!
        array(
            'completed' => $completed, // This value would be accessible in JS using var sc_completed.completed
        )
    );

    // Make sure you reset $wp_query global. If not you might have trouble somewhere else in your code.
    wp_reset_query();
}

function enqueue_scount_script() {
    wp_enqueue_script( 'scount' );
}

add_action( 'wp_enqueue_scripts', 'register_scount_script' );
add_action( 'wp_enqueue_scripts', 'localize_scount_script_first_method', 11 );
//add_action( 'wp_enqueue_scripts', 'localize_scount_script_sec_method', 11 );
add_action( 'wp_enqueue_scripts', 'enqueue_scount_script', 12 );

Make sure you always enqueue/register/localize scripts making use of wp_enqueue_scripts action hook.