You could try opening the output file first, using PerlIO::gzip so that it gets compressed on output, then pass the file handle to Archive::Tar->write() -- something like this:

use PerlIO::gzip;
use Archive::tar;

# ...

open( my $tarfh, ">:gzip", "my_tarball.tar.gz" );

# ...

$tar->write( $tarfh );
[download]

(I haven't tried that myself, but that's what I would try.)

UPDATE: (2010-10-18) It seems that PerlIO::gzip should be viewed as superseded by PerlIO::via:gzip. (see PerlIO::gzip or PerlIO::via::gzip).