Argonians change gender as they age, possibly more than once, but it has more to do with the nature of their unique biology. This isn't typical of other races on Tamriel, although it could be copied by magic I'm sure. If you can turn invisible you can change your gender. That second one seems the least of the two feats.
Invisibility is an illusion. Changing your gender would be more of an Alteration spell than an Illusion spell.
As for the Argonians, we've only one piece of evidence, which has not been elaborated on, alluded to, or even directly mentioned, at least as far as I know. Quite frustrating, to be honest. If any such reference to it exists in The Infernal City or anywhere else aside from the racial description of Argonians in Morrowin, I would love to know of it.