These are my tricks for beating Suicidal. Wyndstar already covered a few of them. I think most of it doesn't involve exploiting the AI, it's more about taking advantage of the game mechanics, and would work just fine against a smart human player.
How to crush Suicidal
1) Before the game starts, put your ability points into population growth, morale, and economy. In GC2, money does everything and generating more money will make your civ stronger in all areas. Tax income is the first and primary way of making money, so that's why these three abilities are important. Diplomacy is also a powerful choice if tech trading is on. I haven't tried most super abilities yet, so all I can say so far is that super diplomat is great with tech trading on, and annihilator, hive, breeder, and manipulator look good.
2) Colonize lots of planets, but don't spend all your money because you'll need it to build your economy. The exact process here depends on a lot of game settings and takes some practice to get it right. On a map with only a few planets for you to colonize, buy your colony ships because time is the limiting factor. But on a map with many planets, buy or build factories and build scout ships and colony ships, because money is the limiting factor. If your colony ships have to travel far, consider researching engines. If there are lots of anomalies to grab, consider researching sensor 1 and building survey ships. Space warfare, space militarization, and universal translator can also be useful during colonization. But any research depends on the tech rate you chose, and research bonuses on early planets.
3) Jumpstart your economy. I've got two tricks here. The first is to use 1% military spending and 99% social spending during the colonization phase. This is so colonized planets can immediately begin building infrastructure. Planets that need to build ships clear their social queues and focus on military. This results in only slightly less military production than 100% military spending. The second trick is to reduce taxes at the start of the game to get 100% approval and double pop growth until you almost run out of money. Then jack taxes up to about 50% approval to get lots of money out of your large population. Try to keep your spending at 100%. Build markets on planets that will specialize in economy, but don't build labs and factories until you know you'll be able to fund their production. Stick to low-tech buildings because they have better ratios of power/productioncost and power/maintenance than high tech buildings. You can upgrade them later.
4) Survive through diplomacy. The most efficient way to stay alive is to prevent others from declaring war on you. If someone does attack you, it's a major setback even if you manage to survive. Increase your diplomacy ability (build diplomatic translators), set up trade routes with likely aggressors, choose an alignment to match theirs, trade techs and treaties, give gifts if relations get low, and increase your military rating. This can be done cheaply by building cargo hulls filled with weapons.
This is the one trick that's really exploiting the AI. "Diplomacy ability" and matched alignments are meaningless to a human player, and a smart player would see through the cargo hull ruse. Setting all AIs to max aggression could make the game much harder if it removes this trick.
5) Tech trade. Buy from one AI a tech that many other AIs do not have (preferably pay with a tech that other AIs do have). Then sell that new tech to all AIs that can pay you something for it. The end result of this transaction is that you've got more tech and more money than you had before, and you've evened the playing field among the AIs. You can take this strategy to the extreme by using it as your sole source of tech (so you don't have to build labs), and a major source of money (so you need fewer markets). I think tech trading alone can win you the game, so I often play with it off.
6) Big shifts in spending. Decide what your immediate needs are, and then achieve them as soon as possible by using 100% spending in the appropriate area. This will allow you to immediately fill a weakness, or quickly capitalize on an advantage. You can use the 99% social and 1% military trick here, too. For example, say that you want to go to war. First, research weapon, defense, engine, and miniaturization techs at 100% science spending. Once you have those techs, switch to 100% military to build lots of ships with the new techs. Then when you have enough ships, send them towards the target. As they're moving, research logistics and soldiering techs. When you reach the target, you'll have all top-of-the-line ships with high logistics and soldiering. If you had used 50% research and 50% military the whole time, some ships would have been completed too early (and would be armed with old tech), and some would be completed too late, and would be just leaving your planets. There is one drawback to 100% military spending; it causes more wastage due to overproducing ships. So I will sometimes tune my military spending so my most productive planet wastes nothing, and divert the rest to science spending.
7) Attack. Acquiring more planets is the fastest way to become more powerful, it's faster than researching and building advanced planetary improvements or economy starbases, so you should not wait until after stock markets and industrial sectors to go on the offense. A new planet produces more taxes, industry, and tech, and you get a free tech and whatever military resources the planet currently had. Plus, a successful assault is easy if you're prepared for it. Obviously, build lots of ships that counter theirs and transports. Move your fleets into position near enemy planets and then declare war. You don't have to wipe them out on the first turn, but the goal is to hit them hard before they can react. This is especially easy if their fleets are out of position due to other wars. Planets are generally lightly defended, so attack them and avoid enemy combat fleets when possible. Fast ships are still very useful in DA, though they're weaker and more expensive than in DL.
The problem here isn't that the AI can't counter a surprise attack, it's that there is nothing in the game that can counter it. The attacker has major advantages: he's prepared, he chooses the time and place of the fight, his ships are near the defender's planets, and the defender has no advantages. There is no way the defender can win if their militaries are evenly matched. Compare GC2 to Civilization 4, which has a wide range of bonuses to strength, movement, diplomacy, and economy for the defender. Offensive war is still a powerful strategy in that game.
8) International politics. Identify which civs are major threats, which are likely allies, and which are easy targets, and then treat them accordingly. Appease the threats just enough to keep them off your back and pay them to start wars with each other so they waste resources. Help out your allies so they will be useful if you need them. I like to trade military technologies to them so they will be strong in the short term, and no threat to me in the long run. To easy targets, I like to trade techs that give planetary improvements. They'll have nice stuff when I conquer them. In general, try to play the balance of power. Make sure your strength is increasing quickly (by conquering the easy targets without interference), but the other major powers are too busy fighting each other. If the balance breaks down, try to steal the winner's success by joining their side and taking some of the spoils.