Hi Golden_voice<3! Welcome to the forum.
Persuasive is a great category to glorify God, sharpen your critical thinking skills, and practice your communication and presentation. With regards to finding a Persuasive topic, I described earlier in a different thread:
The single most important action item you can do before you think of a topic, or apply the pen to the parchment, is to pray. Ask the Lord to lead you and guide you to the topic He would like for you to speak on. "I will fetch my knowledge from afar; I will ascribe righteousness to my Maker...Seek ye first the kingdom of God...ask, and it will be given unto you, seek, and you will find...If any of you lacks wisdom, let him ask of God, who gives to all liberally and without reproach, and it will be given to him. But let him ask in faith, with no doubting, for he who doubts is like a wave of the sea driven and tossed by the wind."
With persuasive speeches, you should speak about something that you are passionate about. Something that energizes you, interests you, or something important that you want to communicate to others. You need to convey why the topic you have chosen is relevant to yourself and the lives of your audience; as well as how the audience can take action.
If you care deeply about the topic you have chosen to speak on, it will show. The judges and audience will notice. If you relate the topic both to yourself and to them, backing it up with solid proof, that boosts your ethos (credibility) big time.
Good persuasive topics, therefore, differ from person to person. The topic should be somewhat general enough that anybody can relate to it, but not too broad so that it becomes very difficult to express your thoughts in ten minutes. On the flipside, the topic shouldn't be so narrow that the judges wonder why you spend ten minutes talking about it. "Narrowness" and "broadness" are somewhat in the eye of the beholder, but it's not impossible to determine.
Sara Nimori, for example, won Stoa's NITOC 2011 in persuasive, and her topic was on Japanese internment camps in the 1940's, but from a different perspective than the conventional wisdom. She went out and interviewed people who were actually forced to be in the camps and showed how the historical application still had meaning for people today. She also, as I previously mentioned, drew a stark contrast between the conventional way that some people think of the camps vs. how she responded to it from a Christian perspective. Taking something that might be well-known or not-well-known and possibly giving a different take on it than what most people are used to is an excellent way to craft an attention-grabbing, enthralling persuasive.
Also, the topic needs to be pertinent not just to you, but to the judge/audience. Good persuasives are not necessarily speeches which have to deal with political issues or moral/religious issues (although I have seen many excellent persuasives on both of those topics). Don't necessarily shy away from choosing a more narrow topic (like Abkhazian independence or something crazy like that, lol). Just be sure to relate the topic to your audience. Why is Abkhazian independence such a big deal, anyway? Who does it affect? Will there be reprecussions that positively or negatively impact the audience? If so, why do those results matter?
Good persuasive topics can be boiled down to three "p's:" pertinent, personal and powerful.
If you are up to the challenge, doing a persuasive on a rapidly changing, controversial event or issue might be risky, but it can be done, and it can be done well. I remember when Lincoln Andersen did his persuasive on ObamaCare/the healthcare overhaul, and boy was it good.
Hope this helps!
(Note to mods: this should probably be moved to "Individual Events" discussion.)