This is a case where you can learn from the AI's strategy. When you go to war with an AI- whether the AI comes after you or you come after the AI- the AI will go pay as many other AI civizilations as it can to join in against you. I think I've noticed that in conquests, AI civilizations are more likely to declare war on me if I am involved in another war, whether my enemies have invited them or not. (Perhaps it's a function of one AI perceiving me as weak when I have committed my forces to fighting an enemy on another front.)
The best way to keep the other AI civilizations from dogpiling on you in a war is to invite as many of them as you can do the war before your AI enemy does. It does commit you to fighting the war for 20 turns if you want to keep your reputation clean, but hopefully the more AI civilizations you can get to attack your enemy, the more of the brunt of the war you divert away from yourself and to your allies.
AIs that fight each other early in the game- and have a chance to really mess each other up a bit- tend to stay furious at each other throughout the game. That means in the future, they are more likely to pick fights with each other and less likely to try a gang up on you. AIs at war also slow down their technological advancement pace.
If you are a peacemonger and find yourself in a weak position to counter-strike once a war starts, bribing nearby AI civs to get into the war not only distracts your AI enemy, but, depending on geography, could soften up enemy towns near your borders. Let your AI allies soften up your enemy for 15 turns while you build up your counter-strike force, take soft enemy towns for 5 turns, then decline to renew the alliances and seek peace for yourself (unless more war benefits you at this point).
The last two games I played, AI civs have started early wars against me when they needed to cross neutral civs to get to me. I turned those neutral civs into my allies early on, and they received the brunt of the wars since my enemies had to go through them to get to me. As a result of the early wars, my allies were left in weakened positions and fell behind in the tech race. Though I'm a jerk for doing it- they did become weak defending me- I took advantage of my former allies in their weakened states and annexed the territory without needing a huge army. (And if I didn't, the jerk AI civs who started unprovoked wars with me earlier would have taken my weak former allies, so really I was doing them a favor by annexing them for their protection before the real bad guys invaded them.)
Signing military alliances early and often is one of the strategies the AI does pretty well, so it's definitely a strategy to incorporate into your game.
When it comes to Right of Passage, I'm never agreeing to one with an AI civ again. The first time I did, my AI "ally" just couldn't resist using my rail to take a shot right at my lightly defended capital in the heart of my empire. I was 1 HP away from losing my capital and all the wonders there.
