Displaying just 2 posts from a category?

<?php
$cat_id = get_cat_ID('featured'); //or whatever you want
$args=array(
  'cat' => $cat_id,
  'post_type' => 'post',
  'post_status' => 'publish',
  'posts_per_page' => 2,
  'caller_get_posts'=> 1
);
$my_query = null;
$my_query = new WP_Query($args);
if( $my_query->have_posts() ) {
  echo 'List of two Posts in category featured ';
  while ($my_query->have_posts()) : $my_query->the_post(); ?>
    <p><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></p>
    <?php
  endwhile;
}
wp_reset_query();  // Restore global post data stomped by the_post().
?>

See How do I determine a Post, Page, Category, Tag, Link, Link Category, or User ID? to find your two category IDs, then put those IDs in the include parameter below:

<?php
//print two posts for each of two selected categories
$taxonomy = 'category';
$param_type = 'category__in';
$term_args=array(
  'include' => '1,2',
  'orderby' => 'name',
  'order' => 'ASC'
);
$terms = get_terms($taxonomy,$term_args);
if ($terms) {
  foreach( $terms as $term ) {
    $args=array(
      "$param_type" => array($term->term_id),
      'post_type' => 'post',
      'post_status' => 'publish',
      'posts_per_page' => 2,
      'caller_get_posts'=> 1
      );
    $my_query = null;
    $my_query = new WP_Query($args);
    if( $my_query->have_posts() ) {
      echo 'List of Posts in '.$taxonomy .' '.$term->name;
      while ($my_query->have_posts()) : $my_query->the_post(); ?>
        <p><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></p>
       <?php
      endwhile;
    }
  }
}
wp_reset_query();  // Restore global post data stomped by the_post().
?>