Well ... PUT has been supported by CGI (and hence CGI::Application) since version 3.31 -- I know, it was the fine monks here that helped me create the patch! (REST Webservices and CGI.pm). There's probably a CGI::Application plugin to make it really easy but here's how I've been doing rest services with CGI::Application:

sub setup {
  my $self = shift;
  my $cgi  = $self->query();

  $self->start_mode( $cgi->request_method() );

  $self->run_modes(
    'PUT'       => 'update',
    'GET'       => 'retrieve',
    'POST'      => 'create',
    'DELETE'    => 'delete',
  );
}
[download]