After reaeding greenFox' comment I realised: Substracting isn't necessary!

#!/usr/bin/perl -w
use strict;
use Time::Local;

while (1) {
    print "Enter year (yyyy) and month (mm), separated by a space:";
    chomp(my $input = <STDIN>);
    last if !$input;

    my ($year, $month) = split / /, $input;
    my $dayname = (qw(Sat Sun Mon Tue Wed Thu Fri))[(gmtime(timegm(0,0
+,0,1,$month % 12,$year + $month / 12)))[6]];

    print "The last day of $month/$year will be a $dayname\n";
}
[download]

Simply rotate the daynames...