How do I add a nested conditional within an echo – to use a default image if there isn’t one in the post?

try this

$second_query = new WP_Query( $args );
if ( $second_query->have_posts() ):
   while( $second_query->have_posts() ) : $second_query->the_post(); 

    $attachment_id = get_field('image');
    $size = "customfeatins"; // (thumbnail, medium, large, full or custom size)
    $my_image = wp_get_attachment_image_src( $attachment_id, $size );


    if (!my_image !== ''){ 

      $image = $my_image[0];

    } else {

      $image="http://domain/image_source/your_image.jpg";

    }       

    endif;

        echo '<article>

            <img src="' . $image . '" alt="' . get_the_title() .'" width="136" height="90" />
            <h3>' . get_the_title() .'</h3>
            <p class="date">' . get_the_date() .'</p>

        </article>
        ';

   endwhile;
endif;