How about monkey-patching Data::Dumper?

use Data::Dumper;
use DateTime;
use DateTime::TimeZone;
use Math::BigInt;

$var = {
    number => 1,
    bigint => Math::BigInt->new(),
    datetime => DateTime->now(),
    tz => DateTime::TimeZone->new( name => 'America/Chicago' ),
};

$Data::Dumper::Useperl = 1;
*Data::Dumper::_dump_orig = \&Data::Dumper::_dump;
*Data::Dumper::_dump = sub {
  return "Math::BigInt->new('".$_[1]->bstr()."')"
    if ref $_[1] eq 'Math::BigInt';
  return "rfc822('".$_[1]->strftime("%a, %d %b %Y %H:%M:%S %z")."')"
    if ref $_[1] eq 'DateTime';
  return ref $_[1]
    if (ref $_[1]) =~ /^DateTime::TimeZone::/;
  goto &Data::Dumper::_dump_orig;
};

print Dumper($var);
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Running it returns this:

$VAR1 = {
          'bigint' => Math::BigInt->new('0'),
          'number' => 1,
          'tz' => DateTime::TimeZone::America::Chicago,
          'datetime' => rfc822('Wed, 03 Dec 2008 04:12:53 +0000')
        };
[download]

Note that most people would prefer that you subclass Data::Dumper to do the same thing, but this works if you need something quick and dirty.