There are several ways of reducing your threat level.
1) Data Centers, each one you destroy subtracts 20 AIP
2) AI SuperTerminal (For every 15 seconds you hold this, you reduce your AI progresses by a net of 1) I wouldn't hold it very long If you already have a reduction in AIP from other sources because that reduction determines how many ships pour out of the ST every 15 seconds.
3) Carefully consider what planets you want to take. Make sure you aren't taking a planet for no reason. There should be some reason why you desire this planet. Either it is rich in resources, holds a strategic location for attack/defense, or has some very desirable captureable. Taking every planet from your homeworld to the AI homeworlds is a good way to over-inflate your AIP and give you trouble later on.
4) Avoid using warheads except on key locations. Depending on what warheads you use, they can increase the AIP from 2-50 per pop. Don't use an Armored Warhead(40 AIP) when a lightning warhead(2AIP) will do. If you are nuking more than 1 planet a game, seriously consider alternatives. Not only are you losing 50 AIP for the nuke itself, the warp gate + command station give you at minimum an additional 20AIP. Other captureables on the planet can significantly increase this (e.g. Human settlements add +100 AIP when destroyed)
In addition, if you are having a hard time, you can always lower the AI difficulty in subsequent games. I found that playing with 2 level 8 AIs was very difficult, and I experienced large fleet losses at every planet I attempted to capture. With AIs at the 7.3-7.6 Range, the game suddenly became more enjoyable and less of a grind. As you get more experience, you can increase the difficulty and see how well you do.