You shouldn't add the accessor generation code to the constructor (unless you really want to redefine your accessor methods each time you instantiate DataTable).

Try this:

package DataTable;

# Important!
use strict;
use warnings;

my @ATTRIBUTES_SCALAR = qw(
    tablename
);

my @ATTRIBUTES_ARRAY = qw(
    columns
    datatypes
    lengths
    decimals
    signed
    allownull
    default
    usequote
);

my @ATTRIBUTES_HASH = qw(
    indices
);

sub new {
    my $class = shift;
    my $self = bless {}, $class;
    $self->{$_} = undef for @ATTRIBUTES_SCALAR;
    $self->{$_} = []    for @ATTRIBUTES_ARRAY;
    $self->{$_} = {}    for @ATTRIBUTES_HASH;
    return $self;
}

{

    no strict 'refs';

    for ( @ATTRIBUTES_SCALAR ) {
        my $attribute = $_;
        *{ __PACKAGE__ . '::' . $attribute } = sub {
            my $self = shift;
            $self->{$attribute} = shift if @_;
            return $self->{$attribute};
        };
    }

    for ( @ATTRIBUTES_ARRAY ) {
        my $attribute = $_;
        *{ __PACKAGE__ . '::' . $attribute } = sub {
            my $self = shift;
            @{$self->{$attribute}} = @_ if @_;
            return @{$self->{$attribute}};
        };
    }

    for ( @ATTRIBUTES_HASH ) {
        my $attribute = $_;
        *{ __PACKAGE__ . '::' . $attribute } = sub {
            my $self = shift;
            %{$self->{$attribute}} = @_ if @_;
            return %{$self->{$attribute}};
        };
    }

}

1;

Update: Fixed a typo