I agree with both prior statements. First you need to evaluate your standing in the game in general. If you are weak to start with, your opponents are using good strategy to attack you in South America since that is a relatively easy continent to take and keep and adds only one border. I might have attacked you even if you hadn't done anything to provoke me (unless you were my ally). The key is to prevent this from happening in the first place.
1. Don't let your neighbors get too strong and at the same time don't antagonaize them as to give them an extra reason to attack you.
2. When your neighbors do get stronger, begin the diplomacy process. Even you don't generally have alliances in your game, at least try to get a ceasefire for one or two turns or a "gentlemens'" agreement so you can build your forces a little. Begin diplomacy early before the situation gets out of hand. If you laid the ground work early (you need me, I need you, being the good cop, etc.) once he does get significantly stronger than you, hopefully you'll have a friend anyway.
3. When being nice fails, remember to play the, "if you attck me, I stop at nothing for revenge" card. I use this sometimes to intimidate people to prevent their attacking me. You need to back up your word though and it sounds like you have done that here. After a while, your opponents should see a connection between their invading you and their subsequent failure. You need to really make them pay though and cripple them. Take out their continent, several territories and even a mega-stack or two if you can. Try to get others into the game as well and have them help you finish him off. In one game when a new player backstabbed me, all of the other players collectively eliminated him in my name. I stayed in the game long enough to place higher than him and teach him a lesson.
4. Finally, if you just can't attack because you do have a prfoundly wealer position in hte game, emigrate to a territory that is out of the way, and turtle. Build up your forces slowly out of everyone's way and stay in the game as long you can. Get cards and find a way to last as long as you can. You can get your revenge later, it doesn't have to immediate.