I've won a few games now on maso/tiny/rare, where I had only one planet for a long time. The key seems to be war-mongering:
1) Rush for Trade and send out freighters to the nearest, most powerful, civs.
2) Act broker; buy and sell everything to everyone and try to stay on top. Research whatever the AI doesn't to make sure you always have something to bribe him with. Try to get hold of a trade good. One will do.
3) As soon as the AI's start trading with each other, bribe everyone to start wars on the others. Make sure the minors start wars as well. Prioritize starting wars between trade partners before their trade income has started to grow substantial.
4) Stand by with transports when a minor empties its planet to go to war. It's usually enough with one or two transports for every minor. This gives you a very nice foothold.
5) Stand by with constructors for when resource star bases are destroyed in one of the wars. Play it right and you will soon have resource monopoly.
The AI's will switch to war time economy, wasting a lot of resources building up fleets while you can focus on improving trade, building constructors and research. If you do this carefully you will often be able to restart wars that have just ended, keeping the AI fighting while you sail for victory.
Be careful about letting one AI get ahead. Give the others a tech advantage by trading only with them for a while, and make sure they gang up on the most powerful one.
With this strategy, the war fleet must be about half of the most powerful AI. Since he will only be trading with you due to the constant wars he will be very reluctant to start a war with you. You may actually be able to pull off an alliance win with 3 or 4 AI's!
(This strategy works on all difficulty levels I've tried it on, but it requires a lot of care in the diplomatic contants on maso.)