Displaying Custom Taxonomy Children in Dropdown

You can use get_query_var( 'term' ) to get the current term and get_query_var( 'taxonomy' ) to get the current taxonomy, then all that is left is to use [wp_dropdown_categories()][1] function withchild_ofparameter andtaxonomy` parameter,
so something like this:

//first get the current term
 $current_term = get_term_by( 'slug', get_query_var( 'term' ), get_query_var( 'taxonomy' ) );
//then set the args for wp_dropdown_categories
 $args = array(
    'child_of' => $current_term->term_id,
    'taxonomy' => $current_term->taxonomy,
    ); 
 wp_dropdown_categories( $args );

Done!