This may be obvious but... coffescript isn't able to do anything conceptually you couldn't already do in javascript. Right now your someFunction definition is a local variable, and is not declared as a property on the instance (unlike getText).
When you use '@' within someFunction I'm assuming you expect it to refer to the instance of Example, which would be convenient in your case, however someFunction isn't defined on example.
If you used the => notation it still wouldn't bind it to the instance (it would refer to the class function). Now this may seem inconvenient, or an odd design choice, but its actually consistent. Once again, someFunction isn't on the instance, its defined as a local variable within the Example class function.
If you use ->, '@' refers to javascripts 'this' for that function (which is the local variable and obviously doesn't contain getText). If you use => it refers to javascripts 'this' at the time of the definition, which is at this point the Example class function. The Example instance, which is what you want to refer to, isn't even created yet (though you wish to refer to it).
The reason @ refers to the example instance within functions like getText is because javascripts this keyword refers to the object your defined on. Coffeescript is really no different, other then providing you a convenient syntax of referring to the 'this' at the time of a functions definition.
TLDR:
You can't really accomplish what your looking for, and your probably going to have to give up on the idea of a 'private' function on an instance
The best I can see you doing is what you've already described in your comments above
Example.prototype.getText()
Because the two ways you'll be able to refer to this method are through the instance and the Example.prototype (which the function is defined on). Since your method isn't defined on the instance, then you cannot use 'this'. However if you call the method from the prototype, your getText function will fail anyway.
getText: ->
@text
the @text refers to what getText is defined on, and in this context its the prototype (not the instance). And text is undefined on the prototype.
If you want to have this method function the way you expect your probably going to have to make it not 'private'. Javascript/Coffeescript do not have access modifiers like public and private, a private method is really a function defined in a particular scope. In this case that scope doesn't have access to what you want, and the this keyword doesn't refer to what you need.