Since I've joined this fandom I've always contemplated this idea, and with some bronies already releasing Rap Battles of their own, I figured I should at least put it up for consideration. Because I would love to participate in it, not run it. But if I have too, I will.
The concept is exactly what you think it is. A tournament where bronies are, for the first round, randomly selected to rap battle with another brony. The winners would be voted by the people and by judges, if possible. It would then be randomized again and repeated with the people that are left until a single victor remained.
I've already even contemplated a few rules.
1. Each person has 3 days to submit and record their verse and give it to there competitor. Who will then do the same thing until 4 verses are made. The song would then be mixed and finished by either the person with the song, or someone else who decides to help.
2. If not submitted in 3 days without notification, a forfeit will then be in place and the other will win.
3. If a notification occurs, the deadline will be extended for a maximum of one week. Any later and the person absent will lose.
4. No editing or changing the beat given. If this occurs, you will be disqualified.
5. Mic quality is not an issue unless it seriously affects the verse in a way that makes it impossible to make out your voice.
6. Anyone can join if the think they can. No age limit or discrimination.
7. Verses must include some sort of Pony-Related material. This is a Brony rap tournament after all.

I haven't done everything, and this is just for ideas if someone takes this under their wings. Things like beats and organizing it are way over my head. But if anyone can do it, please do.