Drupal - Customize days that can be clicked on a Calendar popup

You can pass some Datepicker options from php to the date_popup element through the '#datepicker_options' key:

<?php
$form['date'] = array(
  '#title' => t('Pick the desired date'),
  '#type' => 'date_popup',
  '#datepicker_options' => array(
    'minDate' => 0,
  ),
);

With this method you can pass almost any option but those that accept a function as value, as beforeShowDay, the one needed to restrict weekends or holidays according to the answer referenced by Nikit: https://stackoverflow.com/questions/501943/can-the-jquery-ui-datepicker-be-made-to-disable-saturdays-and-sundays-and-holid

Hence, javascript is required. First you need to include a custom js file from your module code:

<?php
drupal_add_js(drupal_get_path('module', 'FOO') . '/FOO.js');

and provide some code in FOO.js to extend the settings set by date_popup module with our own options.

Here's an example that add the basic option to disable weekends for all datepicker widgets in the page:

(function ($) {
Drupal.behaviors.FOO = {
  attach: function (context) {
    for (var id in Drupal.settings.datePopup) {
      Drupal.settings.datePopup[id].settings.beforeShowDay = $.datepicker.noWeekends;
    }
  }
};
})(jQuery);

Extend to holidays is left as an exercise to the reader :)

Note: the three occurences of FOO in my examples doesn't need to be the same literal, ie: you can provide a BAZ behaviour in BAR.js from FOO.module.

Update: to extend the above for custom days availability, just add a function returning true/false for the day received by parameters.

(function ($) {
Drupal.behaviors.FOO = {
  attach: function (context) {
    for (var id in Drupal.settings.datePopup) {
      Drupal.settings.datePopup[id].settings.beforeShowDay = checkDate;
    }
  }
};

function checkDate(date) {
  if ((date.getDate() % 2) == 0) {
    return [false, 'Even days not available'];
  }
  else {
    return [true, 'Odd days are fine'];
  }
}
})(jQuery);

You can find a more complete example in Date Restrictions module.