My buddy and I played a couple of co-op games vs. Apollo AI and we've found that Spying, specifically Steal Technology as a team of 2 Arc sponsors, is absolutely insane for co-op.

Not sure if most people know but Steal Technology grants you a random technology regardless of whether or not your target has actually learned it. In Civ5, stealing techs would eventually become somewhat useless as you passed the AI in tech. Not so in BE and in fact gets stronger as you progress since techs cost more and more beakers.

With Arc you start with incredibly effective spies. If you co-op, you double your number of Spies and subsequently, since you share techs, double the number of techs stolen. If you're both playing Arc, you can each strike up the trade agreement that further increases your Spy effectiveness. It's about 5 turns to Steal Tech with the 3 main trait bonuses. With the base 3 Spies, that's 6 potential techs per 5 turns...

edit: Spy speed bonuses:

• 50% from Ally trade agreement with Arc
• 50% from your own Character trait
• 25% from Subtle Political trait
• 25% from artifact

We absolutely dismantled the AI with a turn 180ish Purity win (and we didn't even run double Arc -- I was dumb and picked Chungsu [hint: they're awful]). By the end, I had 11/18/17 in Affinities (probably even more, I stopped paying attention) and we nearly unlocked every tech on the web. My science per turn was under 100! I had 4 crappy cities with my capital barely reaching 9 pop by the end. But my units were so far advanced compared to the AI that I was taking cities and capitals with a single fucking Marine unit!

So anyway, if you and buddy want to absolutely shit all over Apollo AI in MP, play as 2x Arc (if you want to get even cheesier, have one guy take coastal scanner and the other take the resource scanner).