For the in-bracket example, you could extract the contents of the brackets, then search through the extracted contents for 'y'. That problem is also very well suited for parsers:

use strict;
use warnings;

my $count;

local $_ = "<Pooh,> said Rabbit kindly, <you haven't any brain>  <I kn
+ow,> said Pooh humbly.";


our $c = 0;

/
   ^
   (?:
      # Outside of brackets
      [^<]

      |

      # Inside of brackets
      <
         [^y>]*
         (?:
            y (?{ local $c = $c + 1 })
            [^y>]*
         )*
      >?  # Optional in case of unmatched bracket.
   )*
   $
   (?{ $count = $c })  # Save count.
/x;

print("$count\n");
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Since the above will match every string without ever backtracking, using $c is optional. You can replace (?{ local $c = $c + 1 }) with (?{ $count++ }) and drop (?{ $count = $c }).

Sorry, I don't have any general solutions.

Update: Fixed a bug in the regexp.