I know how you can get a cell by date and change its color.
You should see this: https://github.com/arshaw/fullcalendar/pull/26
All you have to do is find the plugin for this line:
cell.find('div.fc-day-number').text(date.getDate());
And then you should insert the line below:
cell.attr('data-date', $.fullCalendar.formatDate(date, "yyyyMMdd"));
After that, you can get the cell by date using something similar to this:
$(".fc-widget-content[data-date='20120105']").addClass("disabled-slot");
And put the desired color in the cell.
To disable the cell, perhaps you could do something like this (not tested):
$(".fc-widget-content[data-date='20120105']").draggable({ disabled: true });
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