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
    }
}