This is wrong:

use Date::Manip::Date;

my $date = "2011-07-24T17:46:33Z";
...
my $err = $date->convert([$localzone]);
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Before you can call methods, you first need to create an object:

my $date = new Date::Manip::Date;
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Then you need to set the date & time value into that object using the appropriate method(s).

Then you need to invoke the convert method passing a timezone in one of the formats documented within the modules POD.

Try reading the POD.