snippet to use the term featured image as the post featured image on blog/archive pages, if the post has no featured image of its own. Requires the Display Featured Image for Genesis plugin.

functions.php

<?php

// do not include the opening tag!

add_action( 'genesis_entry_content', 'rgc_add_term_image_archives' );
function rgc_add_term_image_archives() {
	if ( ! is_home() && ! is_archive() ) {
		return;
	}

	if ( ! has_post_thumbnail() ) {
		$taxonomies = get_taxonomies();
		$args       = array( 'orderby' => 'count', 'order' => 'DESC' );
		$terms      = wp_get_object_terms( get_the_ID(), $taxonomies, $args );
		$image_id   = '';

		foreach ( $terms as $term ) {
		  $t_id = $term->term_id;
			$term_meta = get_option( "displayfeaturedimagegenesis_$t_id" );
			if ( ! empty( $term_meta['term_image'] ) ) {
				$image_id = Display_Featured_Image_Genesis_Common::get_image_id( $term_meta['term_image'] );
				break;
			}
		}

		if ( ! empty( $image_id ) ) {
			$image_source = wp_get_attachment_image_src( $image_id, 'medium' );
			$image        = '<img src="' . esc_url( $image_source[0] ) . '" class="alignright" />';
			echo $image;
		}
	}
}