There's no efficient way to compress text streams in pure Perl. Best bet would be to use Compress::Zlib (which is lots better than calling gzip). It wouldn't be too surprising if your installation included it.

my $compressedData =
  Compress::Zlib::memGzip($uncompressedData);
my $uncompressedData2 =
  Compress::Zlib::memGunzip($compressedData);
[download]

I don't understand what the problem with "installing modules" is; if you can write to a directory to install your program, you can install the (pieces of the) module to the same directory (in subdirectories) and push the appropriate paths onto @INC. I'm sure there's descriptions elsewhere on PM as to how to do that. Note that Compress::Zlib has got several pieces that will need to be installed:

/usr/lib/perl5/site_perl/5.6.1/i686-linux/auto/Compress/Zlib
/usr/lib/perl5/site_perl/5.6.1/i686-linux/auto/Compress/Zlib/Zlib.bs
/usr/lib/perl5/site_perl/5.6.1/i686-linux/auto/Compress/Zlib/Zlib.so
/usr/lib/perl5/site_perl/5.6.1/i686-linux/auto/Compress/Zlib/autosplit.ix
/usr/lib/perl5/site_perl/5.6.1/i686-linux/auto/Compress/Zlib/.packlist
/usr/lib/perl5/site_perl/5.6.1/i686-linux/Compress/Zlib.pm

Of course, you'd put them in your own directories.