Sparrow doesn't have anything high-level to handle objects with multiple animations (generally what I call a "Sprite," though Sparrow's meaning of the word is different). You're left to manage that on your own, potentially with what alex_h suggested.
Personally, I wouldn't extend SPMovieClip for this, as what you're looking for isn't a movie clip but a collection of movie clips that you can switch between. I would instead create a subclass of SPSprite that contains multiple SPMovieClip objects and switch between those as necessary (or create them on the fly).
You could roll that functionality into your Player class, but since it's something you're extremely likely to reuse (ie: for enemies), I would go ahead and make something a bit more general.