I'm fond of wrapping the method call into a subroutine reference.

my $cb = MIS_PrintStatus->new();
my $callback = sub { $cb->printit(); };
# ...
my $handler = MIS_SAX_Parser->new($callback);
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Update: I typed too slow and others got this answer before me. I'll try to add some value to this comment by pointing out that you can streamline your constructor:

# Here's what you have.
sub new {
 my ($class, $callback) = @_;
 my $self  = { COUNTER => 0, HASHTYPE => TYPE0 };
 bless $self, $class;
 if ($callback) {
  $self->{CALLBACK} = \&$callback;
 } else {
  $self->{CALLBACK} = \&nocall;
 }
 return $self;
}

# Start with this instead, maybe
sub new {
 my ($class, $callback) = @_;
 $callback ||= \&nocall;
 my $self  = { 
  COUNTER  => 0, 
  HASHTYPE => TYPE0,
  CALLBACK => $callback, 
 };

 bless $self, $class;
}
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