It sounds like you're generally taking the right tack on this - explaining your reasoning calmly. You don't give a lot of other details, so some of these may be what you're already doing, but here's what I'd do.
What you might want to do as the next step, if you're not already doing this, is let your child know when, or under what conditions, she will be allowed to watch the show. It might be in a year or two, it might be not until she's an adult - but having that point be known will help, because when she asks you can simply point to that. Let's say this is something like Supernatural, which is probably not appropriate for a 10 year old but may be for a 13 year old. After you've told her she can watch it when she's 13, if she asks again, you can simply say "Dear, are you 13 yet?" or variations of that - reminding her of the point at which she can watch it.
Another consideration is if this is a series based on a book - like Game of Thrones or True Blood - to suggest she reads the book. Those are both series that probably aren't appropriate for a preteen, but the books are perhaps manageable for some that age (I'd have read either at that age).
Finally, think about where the source of the conflict arises.
Is this something you watch that she wants to watch? If so, you may want to consider not watching it as one way to deal with the issue, or watching it with friends at their house, and not talking about it around her. If you told me I couldn't watch something, but then talked about yourself watching it around me, I'd be annoyed too. Alternately, you could agree to tell her what happens in each episode if she wants to know (such as to keep up with her friends), editing out the bits you don't need to tell her about.
On the other hand, is this something her friends watch? That's more difficult, I imagine, since you're telling her you are making a different decision than her friends' parents. If that's the case you might want to clarify that in the question as that kind of advice is fairly specific to that issue.
Finally, if she's just persistent, you might try to find other ways to redirect. If another show in the same genre isn't helping, you might try other activities - such as games, books, or even writing about the characters or story behind the TV series. Odds are you can find some way to tell her about the plot and/or the characters - a book, a comic book, a plot summary online, or even a personally delivered plot summary like above.