gistfile1.pl

#!/usr/bin/perl

use strict;
use warnings FATAL => 'all';
use feature 'say';

use Moment;

my @weekdays = qw(
    monday
    tuesday
    wednesday
    thursday
    friday
    saturday
    sunday
);

foreach my $weekday (@weekdays) {

    while (1) {
        my $current_timestamp = Moment->now()->get_timestamp();
        my $random_timestamp = int(rand($current_timestamp));

        my $random_moment = Moment->new( timestamp => $random_timestamp);

        if ($random_moment->get_weekday_name() eq $weekday) {
            say $random_moment->get_dt()
                . " "
                . $random_moment->get_weekday_name()
                ;
            last;
        };
    }

}
__END__

output:

1990-10-22 03:12:17 monday
2010-11-02 04:26:12 tuesday
2000-12-06 21:25:42 wednesday
2011-11-10 20:19:28 thursday
1992-01-10 20:10:25 friday
1995-01-07 17:48:43 saturday
1995-11-19 18:59:37 sunday