A few extra tips for keeping the heat off of you.
1) Try to set the AIs against each other. In my experience, paying them to attack each other is MUCH better in the long run that just giving them free stuff. Make sure to pick too guys of about the same strength so it will end up i na stalemate though, rather than a strong guy wiping out a weaking and becoming even stronger. The more they fight each other, the weaker they both become, and they'll be too busy to bother with you.
2) Build attack only ships (no defence/armour/etc) and have them in orbit around your planets. Also get the techs (can't remember them offhand) for a spin control centre and put that on a planet with a lot of strong ships.
3) Trade trade trade (routes). In theory trade is more about making money, but those other civs just LOVE getting free money from trade routes with you. Send as many as you can to the more threatening civs to keep them happy with you. Sure you're making them stronger (trade revenue with you), but you're getting money too, and at least they're not attacking you!
4) Trade trade trade (techs). Once v1.1 is released you can opt to disable tech trade, or at the moment, just trade every non-diplomacy tech you have with everyone else. Research the diplomacy techs and keep them to yourself so you get better deals from this.
Beyond that, just practice, and lower the difficulty level a notch. You're asking questions on how to play better rather than being a bad loser ("this game sucks omg the AI cheats!!!!oneone"). Like anything, practice makes perfect.