one post per term taxonomy

Yeah sure.

<?php 
                    $included_post_ids =array();
                    $args = array(
                      'post_type' => 'APP_POST_TYPE',
                      'post_status' => 'publish',
                      'posts_per_page' => 1,
                      'tax_query' => array( 

                          array(
                          'taxonomy' => 'coupon_category', // Taxonomy
                          'field'    => 'slug',
                          'terms'    => $tax[0]->slug, // Your category slug
                          ),
                    ),
                  );
                  $custom_posts = get_posts( $args );
                  if( !empty( $custom_posts ) ){
                    foreach ($custom_posts as $key => $postObj) {
                      $included_post_ids[] = $postObj->ID;
                    }
                  }
                  //Similar proceduce for other taxonomies 
                  $args = array(
                    'post__in' => $included_post_ids,
                    'post_type' => 'APP_POST_TYPE',
                  )
                  $final_posts = new WP_Query( $args );
                  if ( $final_posts->have_posts() ) {
                  }

?>