Legendaries are a rather touchy subject around here, something that I don't really understand. People claim that they are too often poorly portrayed and are incredibly overused. If that's the case, I'd like to request that we have similar threads wondering whether it would be appropriate to have a story involving a young girl about to begin on a pokemon journey--after all, there are so many 'fics in which such a character becomes a Mary-Sue! Such things are so hard to handle. People just shouldn't write them at all! Or better yet, they must write them in a certain way--you're not allowed to have a character that's particularly bright or pretty or talented, because OMG, that's so totally a Mary-Sue! No one could possibly write a 'fic with such a character that wasn't horrible!
The same goes for legendaries. I encourage to use them however you want, provided that they have some relevance to the story. There's no reason not to have your character capture a legendary--provided that it fits with your canonical views. Obviously, some people here do not believe that this is possible. This is not fact, however--it is only their opinion. There is no canonical evidence that legendaries cannot be caught; indeed, quite the contrary. If you believe as such, it's perfectly fine to not let legendaries be captured in your own story, but if you want them to be, then do so. There's no one who can tell you that it's wrong, as long as it makes sense in the story and you show the consequences of this action.
Remember, too, that there's no rule that says that legends are indeed so highly revered as fanfiction authors often portray them. There is no real indication that they are gods, or even that people worship them as gods. They are shown respect, true, and are believed to be extremely powerful, but if you don't want to make them so almighty, there is no reason to do so. Many authors simply portray them as incredibly rare creatures, so rare that there's believed to be only one and stronger than most normal pokemon, but otherwise nothing particularly special. This angle would make it easier to work with a legend, obviously, but only if you subscribe to the idea.
If you want to work with legendaries, then I encourage you to do so, provided that you do so well. Anything is a viable premise; all that makes or breaks a story is sophistication of writing. I wouldn't let anyone discourage you from using legends in a story if you believe that you are ready to handle them. You are the author of the story, and you must do what you think is best for it. If you think that including a legend is necessary, then do so. Otherwise, do not. Handle them how you please, but write well and consider carefully your views as you do so in order that your story makes sense and portrays them as you please.
To the rest of you: WTF is with going on about how canon misrepresents legendaries? Canon is canon. It is the way things are. Period. If you don't like it, tough. Come up with your own interpretation. Yes, canon shows that people can befriend legendaries. And guess what? Then it must be so. You cannot shoot someone down for following canon, provided that they handle it in a mature and well-thought-out manner. You did not create pokemon. You have no right to dictate how legendaries are portrayed canonically. Don't go all Harmonian on me, plz.
So in short... write what you wish to write, and write it well.