Implicit in the question is the assumption that we are trying to produce an English translation that best captures the nuance of the original Greek without importing any doctrine. In other words, we want a "literal" translation that's useful for interpretation. There are two translation issues here and we can easily separate them and look at them individually:
Junia or Junias?
If you look at the translation of this word in isolation, the obvious translation is "Junia". Here's the NET Bible translator's note:
The feminine name Junia, though common in Latin, is quite rare in Greek (apparently only three instances of it occur in Greek literature outside Rom 16:7, according to the data in the TLG [D. Moo, Romans [NICNT], 922]). The masculine Junias (as a contraction for Junianas), however, is rarer still: Only one instance of the masculine name is known in extant Greek literature (Epiphanius mentions Junias in his Index discipulorum 125). Further, since there are apparently other husband-wife teams mentioned in this salutation (Prisca and Aquila [v. 3], Philologus and Julia [v. 15]), it might be natural to think of Junia as a feminine name. (This ought not be pressed too far, however, for in v. 12 all three individuals are women [though the first two are linked together], and in vv. 9-11 all the individuals are men.) In Greek only a difference of accent distinguishes between Junias (male) and Junia (female). If it refers to a woman, it is possible (1) that she had the gift of apostleship (not the office), or (2) that she was not an apostle but along with Andronicus was esteemed by (or among) the apostles. As well, the term “prominent” probably means “well known,” suggesting that Andronicus and Junia(s) were well known to the apostles (see note on the phrase “well known” which follows).
Notice that the only reason given for preferring the masculine translation over the feminine one is that the rest of the verse might suggest a woman was called an apostle by Paul. The rather embarrassing explanations for how that could "work" are "(1) that she had the gift of apostleship (not the office), or (2) that she was not an apostle but along with Andronicus was esteemed by (or among) the apostles." Neither is a bad explanation if we presume that woman can't be apostles, but that's the a question for interpretation, not translation. Therefore: "Junia".
Among the apostles or known by them?
When it comes to Greek, I'm out of my depth and must lean on experts in the field. I've read the NET Bible note, a comment by Ben Witherington, and a book edited by John Piper and Wayne Grudem. My conclusion is that the Greek is not clear. Paul is paying the pair a high compliment, but whether he considers them Apostles or just known to the Apostles is highly debatable even among those who know best.
In this situation, the best translation preserves the ambiguity. The translation that seems to be open to either interpretation equally is "who are of note among the apostles", which is what the New King James uses. It could mean they are notable apostles or it could mean that the apostles have noted them. The phrase seems open to either reading equally.
Summary
The best doctrinally neutral translation is:
Greet Andronicus and Junia, my countrymen and my fellow prisoners, who are of note among the apostles, who also were in Christ before me.
New King James Version
