This may be obvious, but ... coffescript cannot do anything conceptually, which you could no longer do in javascript. Currently, the definition of someFunction is a local variable and is not declared as an instance property (unlike getText).
When you use the "@" inside someFunction, I assume that you expect it to refer to an instance of the example, which would be convenient in your case, however someFunction is not defined in the example.
If you used obvalue =>, it still would not bind it to the instance (this applies to the class function). Now this may seem like an uncomfortable or odd choice of design, but its actually consistent. Once again, someFunction is not in the instance; it is defined as a local variable in the function of the Example class.
If you use β, '@' refers to javascripts 'this' for this function (which is a local variable and obviously does not contain getText). If you use =>, this refers to javascripts 'this' during the definition, which is currently a function of the Example class. The Example instance that you want to refer to has not yet been created (although you want to reference it).
Reason @ refers to an example instance inside functions such as getText, because javascripts this keyword refers to the object on which you defined. Coffeescript is actually no different, and the other provides you with convenient syntax for referencing 'this' when defining functions.
TL; DR:
You cannot accomplish what you are looking for, and you may have to abandon the idea of ββthe 'private' function on the instance. The best thing I see what you do is what you already described in your comments above Example.prototype.getText() Since the two ways you can access this method are an instance and Example.prototype (which is defined by a function). Since your method is not defined on the instance, you cannot use 'this'. However, if you call the method from the prototype, your getText function will fail.
getText: -> @text
@text refers to what getText defines, and in this context its prototype (and not the instance). And the text is undefined on the prototype.
If you want this method to function as you expect, you probably have to do it not 'private'. Javascript / Coffeescript do not have access modifiers such as public and private, a private method is really a function defined in a specific area. In this case, this area does not have access to what you want, and this keyword does not apply to what you need.