That's what you asked for..
find
<foreach loop="forums:$_data['forum_data'] as $forum_id => $forum_data">
change to
<php>$count=0;</php><foreach loop="forums:$_data['forum_data'] as $forum_id => $forum_data"><php>$count++;if(($count%2)==0){$color='style="background-color: lightgreen;"';}else{$color='style="background-color: lightblue;"';}</php>
Now find all those classes class='col_c_icon' , class='col_c_forum' , class='col_c_stats stats' in the forums if statement and add the {$color} until you get it the way you want it.