function previous_posts_link_class($attr) {
  return 'class="previouspostslink"';
}
add_filter('previous_posts_link_attributes','previous_posts_link_class',10,1);
 
function next_posts_link_class($attr) {
  return 'class="nextpostslink"';
}
add_filter('next_posts_link_attributes','next_posts_link_class',10,1);