package Parent;
...
sub AUTOLOAD {
    my $self = shift @_;
    (my $method = $AUTOLOAD) =~ s/^.*:://;
    return if $method eq "DESTROY";

    if ( $method eq 'parent_method' ) {
         # do something
    }
}

...

package Child;
...
sub AUTOLOAD {
    my $self = shift @_;
    (my $method = $AUTOLOAD) =~ s/^.*:://;
    return if $method eq "DESTROY";

    if ( $method eq 'child_method' ) {
         # do something
    }
}

##</code><code>##

package Child;
...
sub AUTOLOAD {
    my $self = shift @_;
    (my $method = $AUTOLOAD) =~ s/^.*:://;
    return if $method eq "DESTROY";

    if ( $method eq 'child_method' ) {
         # do something
    }
    ...
    else {
         $self->SUPER::AUTOLOAD($method, @_);
    }
}

##</code><code>##

package Parent;
...
sub AUTOLOAD {
        my $self = shift @_;

        my $method;
        if ( defined $AUTOLOAD ) {
            ($method = $AUTOLOAD) =~ s/.*:://;
        }
        else {
            $method = shift @_;
        }
...
}

##</code><code>##

# in Child::AUTOLOAD()
# instead of $self->SUPER::AUTOLOAD($method, @_);

   my $super_method = 'SUPER::' . $method;
   $self->$super_method(@_);