Just to update: in order to get this to work, I had to add the php alchymyth provided into the <a> tagset, like this:
<h2 class="entry-title"><a class="<?php echo (($wp_query->current_post%2 == 0) ? 'red-title' : 'blue-title'); ?>" href="<?php the_permalink(); ?>" title="<?php printf( esc_attr__( 'Permalink to %s', 'twentyten' ), the_title_attribute( 'echo=0' ) ); ?>" rel="bookmark"><?php the_title(); ?></a></h2>
I also had to add and change things in the css of course.
So client will be happy.... next thing of course is that he'll want the single page title in the red and blue instead of black.... I might have to "just say no" at that point!