How can I improve function definition and manage scope better in javascript?

I often use jQuery plugins for front-end functionality in web applications. This requires me to write code like this, where I am assigning a function to a an object property:

var trainingDiary = $("#training_diary").fullCalendar({
  dayClick: function(date, allDay, jsEvent, view) {

    var title = prompt('Event Title:');
    var dayObj = $(this);
    //console.log($(this));
    if (title) {
     $.ajax({
      url: "/app_dev.php/addtrainingday",
      global: false,
      type: "POST",
      data: "dayNo=" + date.getDate(), //returns day of month. getDay() returns day of week
      async:true,
      success: function(msg) {

               trainingDiary.fullCalendar('renderEvent',
                {
                  title: title,
                  start: date,
                  allDay: allDay,
                  backgroundColor:'#cccccc'
                },
            true // make the event "stick" across calendar pages
          )

      dayObj.css({'background-color':'#339933','background-image':'url()'})
      console.log(msg.valueOf());
      } //end ajax success
     })
   } else {
      trainingDiary.fullCalendar('unselect');
   }

  },

  theme: true,
  header: {left:'title',
            center: '',
            right: 'today prev next'},
  firstDay:1

});

The code becomes hard to read and maintain as there is now a success function within an ajax function within yet another function. My question is how can I improve the code so that 'dayClick: function(...) can call a function defined outside of the fullCalendar call. In this case, fullCalendar is a jQuery plugin.

UPDATED CODE:

// Directives for JSLint
/*global console, prompt, $, ROOT_URL */ // declaration of global variables used
/*jslint unparam: true, sloppy: true, white: true */ // disable less useful checks


//create a closure for private scope

  ( function() {

    var calendarOptions, // object, options for calendar diary
        trainingDiary,   // object, training diary using jQuery plugin fullCalendar()
        bgColour = '#339933';

    // Function: onDayClick(day, allDay, jsEvent, view)
    // Callback for the selection of a day in the calendar.
    //
    // Parameters:
    //   date - type?, description?
    //   allDay - type?, description?
    //   jsEvent - type?, description?
    //   view - type?, description?

    function onDayClick(date, allDay, jsEvent, view) {

      var date2 = new Date(date.getFullYear(), date.getMonth(), date.getDate()+1),
          todaysEvents = trainingDiary.fullCalendar('clientEvents', function(event) {
            return event.start >= date && event.start < date2;
          }),
          title,       // string, event title, input by user
          dayObj = $(this),      // object, jQuerified DOM element
          ajaxOptionsAdd, // object, options for AJAX call to addtrainingday script
          ajaxOptionsRemove; // object, options for AJAX call to addtrainingday script

      //NESTED AJAX CALLS - NESTED TO RETAIN REQUIRED PARAMS IN CLOSURE SCOPE

      // Function: onAjaxSuccessAdd(msg)
      // Callback for a successful AJAX call to server-side addtrainingday script.
      //
      // Parameter:
      //   msg - string, message received from server

      function onAjaxSuccessAdd(msg) {

        var event = {
          title: title,
          start: date,
          allDay: allDay,
          backgroundColor: bgColour
        };

        //render the event on the calendar
        trainingDiary.fullCalendar(
          'renderEvent',
          event,
          true // make the event "stick" across calendar pages
        );

        dayObj.css({
          'background-color':bgColour,
          'background-image':'url()'
        }); // added missing semicolon

        console.log(msg.valueOf());

      } // end of onAjaxSuccessAdd declaration

      // Function: onAjaxSuccessRemove(msg)
      // Callback for a successful AJAX call to server-side removetrainingday script.
      //
      // Parameter:
      //   msg - string, message received from server

      function onAjaxSuccessRemove(msg) {

        trainingDiary.fullCalendar('removeEvents',todaysEvents.id);
        dayObj.css({
          'background-color':'#FFFFFF',
          'background-image':'url()'
        }); // added missing semicolon

        console.log(msg.valueOf());

      } // end of onAjaxSuccessRemove declaration

      // AJAX CALL OPTIONS

      ajaxOptionsAdd = {
        url: ROOT_URL+"addtrainingday",
        global: false,
        type: "POST",
        // getDate() returns day of month. getDay() returns day of week
        data: "date=" + $.fullCalendar.formatDate(date, 'yyyy-MM-dd hh:mm:ss'),
          async: true,
          success: onAjaxSuccessAdd
      };

      ajaxOptionsRemove = {
        url: ROOT_URL+"removetrainingday",
        global: false,
        type: "POST",
        // getDate() returns day of month. getDay() returns day of week
        data: "date=" + $.fullCalendar.formatDate(date, 'yyyy-MM-dd hh:mm:ss'),
          async: true,
          success: onAjaxSuccessRemove
      };

      // DAYCLICK EXECUTION LOGIC

      if (todaysEvents.length > 0 ) {
         $.ajax(ajaxOptionsRemove);
         return;
      }

      title = prompt('Event Title:');
      if (title) {
        $.ajax(ajaxOptionsAdd);
      } else {
        trainingDiary.fullCalendar('unselect');
      }


    } // end of onDayClick declaration

  // CALENDAR INITIIALIZATION CODE

  calendarOptions = {
    dayClick: onDayClick,
    theme: true,
    header: {
      left: 'title',
      center: '',
      right: 'today prev next'
    },
    firstDay: 1,
    eventRender: function (event, element) {
      element.removeClass('fc-corner-right fc-corner-left'); //removes border round the event
    }
  };

  trainingDiary = $("#training_diary").fullCalendar(calendarOptions);


}() ); //end of and call of closure