Solution 1:

classes are just functions so they create scopes. everything defined inside this scope won't be visible from the outside.

class Foo
  # this will be our private method. it is invisible
  # outside of the current scope
  foo = -> "foo"

  # this will be our public method.
  # note that it is defined with ':' and not '='
  # '=' creates a *local* variable
  # : adds a property to the class prototype
  bar: -> foo()

c = new Foo

# this will return "foo"
c.bar()

# this will crash
c.foo

coffeescript compiles this into the following:

(function() {
  var Foo, c;

  Foo = (function() {
    var foo;

    function Foo() {}

    foo = function() {
      return "foo";
    };

    Foo.prototype.bar = function() {
      return foo();
    };

    return Foo;

  })();

  c = new Foo;

  c.bar();

  c.foo();

}).call(this);

Solution 2:

Is it even possible without getting "fancy"?

Sad to say, you'd have to be fancy.

class Thing extends EventEmitter
  constructor: (name) ->
    @getName = -> name

Remember, "It's just JavaScript."

Solution 3:

I'd like to show something even fancier

class Thing extends EventEmitter
  constructor: ( nm) ->
    _name = nm
    Object.defineProperty @, 'name',
      get: ->
        _name
      set: (val) ->
        _name = val
      enumerable: true
      configurable: true

Now you can do

t = new Thing( 'Dropin')
#  members can be accessed like properties with the protection from getter/setter functions!
t.name = 'Dragout'  
console.log t.name
# no way to access the private member
console.log t._name