That doesn't look very deterministic to me! The following code may work a little more efficiently with large strings:

use strict;
use warnings;

my $incrsdel = 10;
my $str = "acbcybaycayacyccy";
my @chrs = split '', $str;
my $yTot = $str =~ tr/y//;

for my $letter ('a', 'c') {
    $yTot += subLetter ($letter, $incrsdel - $yTot, \@chrs);
    last if $yTot >= $incrsdel;
}

$str = join '', @chrs;
print "$str\n";


sub subLetter {
    my ($letter, $limit, $chrs) = @_;
    my @letPos = grep {$chrs[$_] eq $letter} 0 .. $#$chrs;
    my $count = 0;
    
    while ($count < $limit && @letPos) {
        $chrs->[$letPos[my $idx = rand @letPos]] = 'y';
        splice @letPos, $idx, 1;
        ++$count;
    }
    
    return $count;
}
[download]

Oh, and it scales to a larger set of replaceable characters easily too.