Well, as a matter of fact, the type of goggles she wears when she is competing with her rivals is not different from other kinds of goggles. However, since she is to some extent slightly nearsighted, her goggles has prescription and is polarized. Actually, there would be no different between different types. But swimmers always choose to wear water tight goggles which are also anti-fog.
The goggles Natalie Coughlin wears are femme eclipse from TYR. If you want to wear the similar type, you could go to the online stores to have a search. The price online may be cheaper than those in the real stores. And the quality is just as same as those in the real stores.