Show one post of each custom taxonomy

assuming all your constants are correct, it should just look like this

$terms = get_terms(array('taxonomy' => APP_TAX_STORE));
$tax = get_the_terms($id, 'coupon_category');
foreach ($terms as $term) {
    $args = array(
        'post_type'      => APP_POST_TYPE,
        'posts_per_page' => '1',
        APP_TAX_TAG      => 'gutschein',
        'orderby'        => array(
            'meta_value_num' => 'DESC',
            'post_date'      => 'DESC',
        ),
        'tax_query'      => array(
            'relation' => 'AND',
            array(
                'taxonomy' => 'coupon_category',
                'field'    => 'slug',
                'terms'    => $tax[0]->slug,
            ),
            array(
                'taxonomy' => APP_TAX_STORE,
                'field'    => 'slug',
                'terms'    => $term->slug,
            ),
        )
    );
    $new_query = new WP_Query ($args);
    if ($new_query->have_posts()) {
        while ($new_query->have_posts()) {
            $new_query->the_post();
            get_template_part('loop', 'coupon');

        }
    }

}