Hmm, as far as I know you just enter the domain you want it to be valid for, presumably your subdomain.
With CGI.pm:

$cookie = $query->cookie(-name=>'name',
                         -value=>'value',
                         -expires=>'expcode',
                         -path=>'partial_url',
                         -domain=>'domain_name'
                         -secure=>1);
print $query->header(-cookie=>$cookie);
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Perl In A Nutshell, page 338

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