I enjoy creating fakemon, although I haven't really had many reasons/chances to include them in fanfics. I really just do it more for the fun of creating my own regions in and of themselves than for inclusion in any writing. I also like reading about them as long as they're handled well; I'm not one for bludgeoning fakemon creators with "you must follow Game Freak's 'traditions' or you suck at making fakemon and nothing you do is valid", like some people I've seen, but they do have to be believable as Pokémon to an extent and in the context of that particular story. (There are a lot more ways to accomplish this than those stuffy traditionalists would have most people believe, but I digress.) It looks obvious and desperate if someone just sticks Super Uber Megadeath Celemanashayjiramewfiftymon in a story for the hell of it, and that's when it gets annoying.
As for your "dilemma", well... I honestly don't think that the "too many legendaries" complaint applies to anything other than the video games (and even then, I personally do not care). Yes, some people say it devalues them, there are people who don't like using/battling them because they're broken and wish GF would put that effort into creating more normal, "fair" Pokémon. But if legendary Pokémon are the Pokémon world's equivalent to gods/deities then they clearly already have a polytheistic "religion"... and most of the real world's well-known polytheistic religions don't just stop at 35 gods, now do they? The Ancient Greeks, the Romans, the Ancient Egyptians, the Norse, the Hindus, the Chinese, the Japanese, the various Native American tribes... dozens, hundreds, thousands of gods each, most of them with their own unique aspects and importance and no one complaining about "too many".
On that note, I've also seen people complaining about how since Arceus is the "supreme god Pokémon", Game Freak has backed itself into a corner and can't possibly create anything else. What else can there be, right? Plenty--if end-all, be-all Arceus was all that was necessary, what's the point of every single other legendary Pokémon that came before it? Why not just introduce the final supreme being at the beginning and be done with all legendaries for the rest of the franchise's life? And didn't most people consider Mew a sort of "supreme" Pokémon until Arceus came along? Ho-Oh, Lugia and Celebi were never intended to "trump" Mew, but they came after it. So why do any further legendaries have to "trump" Arceus? There are clearly plenty of other "jurisdictions" a legendary could have dominion over. A quick look at any other polytheistic religion, or just taking a few minutes to explore your imagination or whatever you feel your story world needs, can easily reveal plenty of other places for legendaries if you are feeling so inclined. (If not, then of course there's no reason to add them at all, but people who say that Arceus has precluded the ability to create any more are being ridiculous and short-sighted.)
(Actually, I have thought of one legendary that can be greater than Arceus, mwahaha, but that's another discussion for another time and I'm not done developing it anyway.)
Depending on the culture you're talking about (and the people/setting in your story), you will want different gods to control different things. These can be major or general things like "creator of the universe" or "god of thunder and lightning", but they can also be more specific or obscure like gods that oversee the seasonal monsoon or that control the growth of specific important crops, things like that. Different regions can have their own specific gods or protectors in addition to more "global" deities. It's possible to create an interesting, non-mundane god without having to resort to something extreme that has probably already been covered by Arceus or Moltres or Azelf anyway.
Not that I'm suggesting that you tack on a whole additional 700 gods to the Pokémon pantheon for your story, of course; I don't know anything about what you're writing, and you said that you're just looking at adding one. But there's no reason that you can't if you feel like you need to!
...and, of course, the argument against more legendaries in non-game applications gets even weaker if you don't want to consider them deities at all, but rather just impressively-powerful Pokémon. In that case, is adding one really any different from adding any other Pokémon?
With all that said, if you still think that creating a new legendary Pokémon for your story might be superfluous, just ask yourself what this legendary is supposed to do and what makes it different/better for the job than the existing ones. If you feel like it's completely redundant, then there may not be a reason to bother with it; if you feel like it brings something new to the table that the existing ones don't and your story won't work with Articuno, Rayquaza or any of the others, then by all means write about it. Don't compromise your story, either by including a fakemon that you don't need or by not including it when what currently exists is insufficient for your fanfic.
...there I go, ranting again. :/ What can I say? I really like mythology, legendaries and fakemon, and when I get started about something I like I suppose there's no shutting me up. Eh.
...I also like "abusing" quotation marks, btw.