Your input is in $line and you're trying to transliterate $nuline without first assigning $line to $nuline. Compare your program with this:

while (my $line = <DATA>) {
    chomp $line;
    (my $nuline = $line) =~ tr/a-zA-Z/n-za-mN-ZA-M/;
    print "$nuline\n";
}

__DATA__
me
you
someone else
[download]

Output:

zr
lbh
fbzrbar ryfr
[download]

update:: output added