Sticking as close as possible to your methodology, but just a more compact representation, this version works.

Working out what small change in your logic was required is left as an exercise :)

#! perl -slw
use strict;

$|++;

my @board = map [ (' ') x 39 ], 1.. 39;
$board[ $_->[ 0 ] ][ $_->[ 1 ] ] = '0'
    for [1,1],[1,2],[2,1],[3,4],[4,3],[4,4],
        [9,8],[9,9],[9,10];

#my @board2 = @board;
printf "iterations: ";
my $z = <stdin>;
$z--;
my $t = 0;

print "t:$t";
$t++;

print join '|', @$_ for @board;

select(undef, undef, undef, 1);

while( $t <= $z ) {
    my @neighbours;
    my $i = 0;
    my @board2;
    for my $row ( @board ) {
        my $j = 0;
        for ( @$row ) {
            local $^W;
            my $neighbours = 0;
            ++$neighbours if $board[$i-1][$j-1] eq '0';
            ++$neighbours if $board[$i-1][$j  ] eq '0';
            ++$neighbours if $board[$i-1][$j+1] eq '0';
            ++$neighbours if $board[$i  ][$j-1] eq '0';
#            ++$neighbours if $board[$i  ][$j  ] eq '0';
            ++$neighbours if $board[$i  ][$j+1] eq '0';
            ++$neighbours if $board[$i+1][$j-1] eq '0';
            ++$neighbours if $board[$i+1][$j  ] eq '0';
            ++$neighbours if $board[$i+1][$j+1] eq '0';

            $board2[$i][$j] = ' ';
            $board2[$i][$j] = ' ' if $board[$i][$j] eq '0' and $neighb
+ours  < 2;
            $board2[$i][$j] = '0' if $board[$i][$j] eq '0' and $neighb
+ours == 2;
            $board2[$i][$j] = '0' if $neighbours == 3;
            $board2[$i][$j] = ' ' if $board[$i][$j] eq '0' and $neighb
+ours  > 3;
            $j++;
        }
        $i++;
    }

    print "t:$t";
    print join '|', @$_ for @board2;

    $t++;
    select(undef, undef, undef, 0.1);
    @board = @board2;
}
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