How to customize the symbols that appear in the Visual Editor insert custom character

The TinyMCE Editor has a great button in the kitchen sink to insert custom characters / symbols.

Is there a way to control what symbols show up in this pop-up? (Specifically I need some unique Hawaiian language characters ‘okina and macrons).

Code    Character
Ā  Ā
ā  ā
Ē  Ē
ē  ē
Ī  Ī
ī  ī
Ō  Ō
ō  ō
Ū  Ū
ū  ū
ʻ  ʻ

Hawaiian Diacritical mark reference:
http://manoa.hawaii.edu/site/hawaiian_language.html

This has to do with your character map for tinyMCE it’s located inside:

wp-includes/js/tinymce/themes/advanced/js/charmap.js

Although I wouldn’t recommend editing the WP-Core you could theoretically just add new characters there like so:

['Ī',     'Ī',  true,'I kahako'],
['Ō',     'Ō',  true,'O kahako'],

and so on…

However when you update WordPress this will overwrite those changes. So it’s not the best solution but it would work.