Pretty simple.

use strict; use warnings; 
my @weekdays = qw(
Today
Yesterday
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
);

my %lookup; 

  my @backs; 
  use Time::Local;

  my ($sec,$min,$hour,$mday,$mon,$year,$wday,$yday,$isdst) =localtime(
+time) ; 
  # move to noon so DST  changes dont kill ya 
  my $now_fix12=timelocal( 0, 0, 12, $mday, $mon, $year);

  for my $back (0..6) { 
    my ($sec,$min,$hour,$mday,$mon,$year,$wday,$yday,$isdst) =localtim
+e(time-24*60*60*$back) ; 
    push @backs,[$wday,$mday]; 
    $lookup{$weekdays[$wday+2]}=$mday; 
    }

  $lookup{'Today'}=$backs[0][1]; 
  $lookup{'Yesterday'}=$backs[1][1]; 

  for my $wday (@weekdays) { print $wday.' '.$lookup{$wday}."\n"; }
[download]

Edit:code fixed to fit changed OP