"Salute A. and J., my kinsmen and my fellow-prisoners, who are of note among the apostles, who also were in Christ before me." (Rom. 16:7)There are two relevant questions: first, is J. a man or a woman; second, is J. an apostle?
Man or Woman?
"Junius" is a well-known Roman surname. Marcus Junius Brutus, for example, is Julius Caesar's famous assassin. Unsurprisingly, it was also used as a personal name, although apparently not very frequently. For men, the personal version would have been "Junias"; for women, the personal name would have been "Junia." Furthermore, "Junias" (male) would also be the typical Greek way to make a nickname from other common male names like Junianus or Julilius (in the same way that "Silas" is a nickname for Silvanus, for example). Finally, it was common practice for slaves -- who were often freed in the ancient world -- to take the surname of their previous master as a personal name upon their release. Freed slaves formerly belonging to the house Junius would commonly be named "Junias" if male or "Junia" if female.
So we have two names: "Junias," a male personal name and nickname for a few different male personal names, and "Junia," a female personal name.
Because of the way the Greek language works, the form of words change when they are used in different contexts. We sometimes do this in English: in the present I "drink" tea, but in the past I "drank" tea. Greek does this constantly. One would say that "Junia greets you" but that "you greet Junian." It's a small but helpful difference that is a great feature of the Greek language (just as it's useful to be able to distinguish between "drink" and "drank" in English).
The problem is that when Junias and Junia are the ones being saluted, you spell their names the same: there is no way to differentiate between "salute Junian" (i.e. Junias the man) and "salute Junian" (i.e. Junia the woman). In Romans 16:7, Paul says to "salute Junian." Is he talking about a man or a woman? There's simply no way to tell.
You will sometimes hear that we have no records from antiquity of the male name "Junias" being used. This is true, but it is also misleading. We have almost no records from antiquity of either personal form -- Junias or Junia -- being used. It so happens that the first century documents that have survived include just one cases of the latter and one ambiguous case (viz., Romans 16:7).
Verdict: there is no way to tell whether the "Junian" Paul mentions is male or female.
Apostle or Not?
The second question is whether Paul is even calling J. an apostle. In the KJV, there is a nice ambiguity in the passage: J. is "of note among the apostles." In English, this could mean that J. is one of the apostles and in fact a noteworthy one; it could also mean that J. is someone who the apostles see as noteworthy. "My blog is of note among the blogs" means something rather different than "my blog is of note among fine readers." For example, in Romans 2:24, Paul says that the name of God is blasphemed among the nations: the name of God is not one of the nations, but rather is an object of blasphemy to them. If you look up the word translated "among" in a Greek dictionary, you will see that it will list both possible meanings. Thus, if this were the end of the story, we would have to conclude this question as we did the first: it is perfectly ambiguous, so there is simply no way to tell.
But this is not the end of the story. The word translated "notable" (ἐπίσημος) has two broad meanings, one comparative (more well known than) and one elative (well known to). If you do a systematic study of how this word is used, it turns out that the Greeks usually made a distinction between these two meanings based on what comes afterward: is what comes afterward is a genitive form (which means here a comparison) or a dative form (which means here "to"). In this passage, the dative is used: A. and J. are well known to the apostles. There is a perfect grammatical parallel in Psalm 2:6, in which the Jews are "a spectacle among the gentiles." The grammatical forms are exactly the same, and the words are even identical (ἐπίσημος can be translated "notable" or "spectacle") except the last word (apostles/gentiles). The Jews, of course, are not gentiles; rather, they are well known (in a negative sense) to the gentiles. The passage in Romans means the same thing: A. and J. are not apostles; rather, they are well known (in a positive sense) to the apostles.
Verdict: whether J. is a man or woman, Paul is distinguishing J. from the apostles, not including J. among the apostles.
