Alex made an excellent post about the use and potentially offensive qualities of the word "cisgender" in queer communities. He's covered all his bases there, and I highly recommend reading for a further exploration of the debate. Instead, I want to take a step back and look at the whole language picture - the nature of the English language - and apply it to queer culture. I'd like to approach both "cisgender" and the neuter pronoun set "hir/zir/zie/etc" in particular.
To be specific, invented words in the queer culture are known as neologisms to linguistics. Neologisms are coined words used by a language community to describe a new action, new concept, or new object. If you've ever read a blog (ding ding!), used a computer, surfed the Internet, or participated in a meme, you are part of a new explosion of neologisms, invented for the sole purpose of explaining a new realm of experiences previously unseen in the English language. Long story short, the neologism stems from one of the basic laws of language: "Language is shared by a community."
Collaboration and the Neologism
Language is, at its core, an act of sharing. Because of this we must share all aspects of the language process -- use, definitions, and language creation - with every other language user in a community. Even though different communities may have different words at their disposal, communities must share words and definitions or else risk not communicating effectively. (First person shooter fans may confuse non-players with their talk of frags, lag, buffs, noscopes, telefrags, n00bcannons, and the interjection "Teams!", but FPS players know what other FPS players are talking about, and that's the only important thing to their communication.) Therefore, like it or not, words will come into being to describe a situation that would otherwise have no descriptive terms, and these words will be accepted into the lexicon by way of common understanding.
In the case of "cisgender," we see a word invented to describe a situation that has not been described properly before. As Alex points out, the word came into existence in lieu of "messier" terms, words that often put trans people into an "Other" class. (Earlier queer literature often refers to "Genetic Girls," "Real Women," "Natural Men," etc.) Cisgender is a term created to fulfill the role of a binary opposition; if you are not gender-variant, you are cisgender. No other term fulfills this role, so cisgender quickly caught on as meaning "opposite of transgender."
There are people who feel that cisgender is an offensive term, and wish for the term to be removed from the queer lexicon. For this, we need to look at why words leave the English language. There are typically two ways a word can leave a language: one, if it no longer serves a purpose; and two, if it becomes a word that the general public sees as offensive. The computer term "punch-card" is an example of the first, as nobody really interacts with computers using punch-cards anymore. For the second, we can look at racial slurs that have slowly shaken out of the system as people began avoiding derogatory speech - the word "Sambo," for instance, is nearing extinction in my region, though it is still a hot-button term in some communities. These words don't disappear, but they do lose their place in common conversation.
On both counts, cisgender fails to meet requirements for removal from the lexicon. We have more need than ever to present an opposite term for "transgender," and few people find it offensive enough to warrant scrubbing the word from the lexicon. We can whine and we can cry, but people will continue to use the term within queer communities. Even if better alternatives are introduced, people will be unwilling to switch over; the new terms lack a shared definition within a community. (For an example, look at the Microsoft Zune's attempt to introduce "squirting" to the technology lexicon. Neat idea, but it never caught on as well as, say, "iPod.")
Shoehorning Words into an Already Packed Language
Cisgender gives us an excellent example of how words get added to the language. They are not planned, nor are they intentional; they just fill a need. Dozens of words have been created to describe queer experiences and now enjoy a permanent place in the lexicon. The other side of queer linguistics, however, has not been so successful. For years I've seen people attempting to shoehorn neutral-gender pronouns into the language.
A quick bit of history here: English did, at one time, have neuter pronouns. These holdovers from the Anglo-Saxon language eventually fell out of use as more strictly gendered borrowed words from Romance languages were layered atop English's Germanic roots. I get the reasoning for neuter pronouns, and I see the cause as noble. However, I also see the pronouns as a failing proposition.
Some parts of language are for the most part immutable. Basic building blocks such as prepositions, pronouns, and conjunctions very rarely see any linguistic shift after they are agreed upon by a language community. The trouble with neutral-gender pronouns is that they attempt to shirk this trend, insisting that normal people change their basic understanding of language and communication to discuss gender-neutral subjects. The logic seems fair enough: if enough people use the term, it will eventually come into common use.
This methodology rarely succeeds. For one, the change is not forced by any "hole" in our lexicon: words exist to cover male and female, and many English speakers don't see the utility of having a gender-neutral pronoun. Second, the gender-neutral pronoun adopters are attempting to change the basic building-blocks of the language. I remarked in a previous post that humans may have hard-wired perceptions of what is male, female, human, and inhuman. The same is true of language; neurolinguistic scholars have documented the "black box" nature of language learning: we do not understand how we learn it, but children in a language community quickly learn the intricacies of communication.
However, language does find its own solutions for holes in communication. The modern fix to the gender-neutral pronoun is the co-opting of the words "they" and "their" when a genderless pronoun is needed. (In the case of formal writing, he/she and s/he seems to take prevalence.) Prescriptive grammar supporters may scowl with anger, but the fact of the matter is that prescriptive grammer must eventually bow to the will of the language speakers. (Take split infinitives as an example; eventually, the grammar police always lose.)
In many ways the gender-neutral pronoun will exist in much the same way "cisgender" or "frag" may appeal to queer or first-person-shooter language groups: people within the community will understand the use of the term, but outsiders will need a little help to "get it."
It is my sincere hope that some honest-to-goodness linguist stumbles upon this and offers some more specific advice. This is admittedly born from a combination of experience, scholarly research, and observation, though I'm far from claiming that I have any documented expertise on the subject.
Please, feel free to drop your hat in the ring with your ideas.