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UPDATE: (2010-10-18) It seems that PerlIO::gzip should be viewed as superseded by PerlIO::via:gzip.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

In reply to Re^3: Problem in sending "tar" files as attachment using MIME::Lite module by graff
in thread Problem in sending "tar" files as attachment using MIME::Lite module by santhi

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