How do I get rid of Rebels without causing an uprising?

Whatever you do in Tropico 5 is going you make you side with 1 faction or another, you'll never reach any sort of utopia, which to lead to Rebels and Rebel leaders in 1 form or another. Which is ironically what makes Tropico actually very realistic.

First, stop banishing Rebels or Rebel leaders, all that's going to do is cause an uprising, you need to bribe the rebels instead. Also change around your Constitution so your not completely favoring 1 faction over the other, which I personally have never perfected. It's pretty much impossible I think.

You can try "social engineering" which takes time, and the "smear campaign" can help as well trying to balance factions out. Amnesty does work, It may not lower the rebel numbers significantly, but it should lower the threat of rebel attacks.

I've seen some people suggest not having Plutocracy - any source of Swiss bank revenue is increased by 20%, in your constitution as well. Others suggestion having a democracy when you enter the modern era. But having a democracy is the hardest way to keep your Island happy to win elections. Hope this helps.

SOLUTION: Here's what I found.

FIRST, try to get all happiness factors (food, job, housing, etc) above 50, this reduces number of new rebels to near zero. However, if of the happiness factor fall below 50, they will spawn everywhere like they always do.

SECOND, if you have rebels and want to get rid of them, DON'T KILL OR BANISH THEM. The more you do this, the more you lose because eventually an uprising happens. Instead, build the Supermax Prison (or the Dungeon I'd imagine works too) and arrest them. This doesn't cause uprisings and the rebels are captured and converted back into good little citizens.

LASTLY, there is no way to completely get rid of rebels, even with 100% perfectness. Any attacks are just a regular (annoying) thing in the game and you just have to build a large military to quickly defeat them. Placing 4 Barracks near 2 Army Bases near 6 Guard Towers should do the trick. Rebels will usually go for the guard towers first and be killed.

Hope this helps. ;)