$ perl -e'
use Data::Dumper;

my %ManagerInCharge = (
    200610 => {
        56 => "jane",
        59 => "john",
        69 => "joe",
        100 => "frank",
        },
    200701 => {
        23 => "abel",
        11 => "gunder",
        37 => "frank",
        },
    );

print Dumper \%ManagerInCharge;

for my $hash ( values %ManagerInCharge ) {
    my $index = 1;
    for my $key ( sort { $a <=> $b } keys %$hash ) {
        $hash->{ $index++ } = delete $hash->{ $key };
        }
    }

print Dumper \%ManagerInCharge;
'
$VAR1 = {
          '200610' => {
                        '69' => 'joe',
                        '59' => 'john',
                        '56' => 'jane',
                        '100' => 'frank'
                      },
          '200701' => {
                        '11' => 'gunder',
                        '37' => 'frank',
                        '23' => 'abel'
                      }
        };
$VAR1 = {
          '200610' => {
                        '4' => 'frank',
                        '1' => 'jane',
                        '3' => 'joe',
                        '2' => 'john'
                      },
          '200701' => {
                        '1' => 'gunder',
                        '3' => 'frank',
                        '2' => 'abel'
                      }
        };
[download]

Update:

Without the nested for loops:

for my $hash ( values %ManagerInCharge ) {
    my $upper = keys %$hash;
    @{ $hash }{ 1 .. $upper } = delete @{ $hash }{ sort { $a <=> $b } 
+keys %$hash };
    }
[download]