Is it possible to have another sidebar for posts page?

The posts use the default layout. It’s best to set the default layout to the layout you wish to use on the bulk of your content.

then you change what you want on the smaller number of pages.

/**
 * Get the custom sidebar for blog pages using Genesis Simple Sidebars
 * 
 * Priority is set to 9 so we set the "default" sidebar to that of the
 * Page for Posts before the Simple Sidebars plugin alters it
 */
add_filter( 'sidebars_widgets', 'my_sidebar_widgets_filter', 9 );
function my_sidebar_widgets_filter( $widgets ) {
	if ( ! ( is_home() || is_singular( 'post' ) || ( is_archive() && ! is_post_type_archive() ) ) )
		return $widgets;
	$page_for_posts = get_option( 'page_for_posts' );
	$sidebars = array(
		'sidebar'      => genesis_get_custom_field( '_ss_sidebar', $page_for_posts ),
		'sidebar-alt'  => genesis_get_custom_field( '_ss_sidebar_alt', $page_for_posts ),
		'header-right' => genesis_get_custom_field( '_ss_header', $page_for_posts ),
	);
	$widgets = Genesis_Simple_Sidebars()->core->swap_widgets( $widgets, $sidebars );
	return $widgets;
}