To OP -- since all you're trying to do is make certain rows a different color, then you can have the code reflect that as well, making it easier to read and maintain:

while ($dy < 32) {
    $table_info .= $q->Tr({
                           -align => 'left',
                           ($dow == 0 || $dow == 6 ? (-color => 'yello
+w') : () ),
                          },
                          $q->th([$...]),
    );
    $dy++;
}
[download]

Then from here, we can go even further and use map (and use "THE DISTRIBUTIVE PROPERTY OF HTML SHORTCUTS" -- see CGI pod):

print OUTPUT $q->table({-cellpadding => 3},
    $q->Tr({-align => 'left'}, [
        map {
          $q->Td( { ($dow == 0 || $dow == 6 ? (-color => 'yellow') : (
+)) },
                [ ... ] )
        } 0 .. 31
    ]),
);
[download]