Japanese, I think I can help, since I'm a major Japanese player... First off, you have to raid the Japanese, or they'll raid you. Their major disadvantage early in the game (ESPECIALLY ON WATER MAPS AND DESERT MAPS) is that they have very poor wood consumption for the amount of wood they have to produce for their major bonus of farming and fishing. Your food is always on the max, but your wood is usually lagging (which sometimes kills me on Great Sahara since I have a woodcutter's camp with three citizens...)
The way to kill them is to raid often, and hit the most unlikely targets... Go for his granaries and lumber mills. First off, before anyone flames me, let me give an example.
***START EXAMPLE***
In the Gunpowder Age, as I the Japanese player, have all ready by now have ten-twelve farms (depends on if I have fishing boats) and two granaries... Each farm produces +13 (25% income bonus on all food producers), so 13*10 = 130 food. This is an automatic +30 food without any upgrades whatsoever. The first granary tech pushes this up to +243 (major jump...), and the next one will make this 325, and the last one will make this an extraordinary, 487.5 food. I usually have this tech by the time I reach Industrial...
Now, if I can kill off both of his granaries and destroy five farms that will give him only +65 food... Now tell me, isn't that a major kill to the Japanese player, who now has to rebuild both granaries (basically around 200 wood and 100 wealth depending) and then have to rebuild farms (more wood...). So, if I can accomplish this with 4 HC and 4 HA, I think I've done a whole crock load to damage to the Japanese player.
***END EXAMPLE***
***DISCLAIMER*** Before reading below, I don't play Mayan, and I usually play Japanese/French, so this is mostly pure speculation and taking tips from games I've played and seen against Mayan. ***END DISCLAIMER***
This leads me to my next point. The Mayan player's major ability is their wood production, right? So, following my example's logic, wouldn't annihilating their lumber mills, farms, and granaries (in that order) be a major determent to a Mayan player. I speculate this, since you can (I imagine) usually sit outside the range of cities and destroy the farms and lumber mills and granaries without coming into range of the Towers and Cities... Their civilians would be garrisoned, but so much the better so that way I won't accidentally have targeted their citizens when wanting to blow up farms and such.
So, maybe the Mayans are overpowered, the BHG staff gave us patch 3 (THANK THE MAKER!!!!) and now their working on an expansion set. I'm trying to find a way to defeat the Mayans without the need to cry and whine about nerfing them. I admit they are overpowered, but if I can beat them with a much lesser nation (i.e. tier system with Japanese and French) doesn't that make me a better player for it?
Have fun with this, and I hope some people really consider what I'm saying and extrapolate on what I'm saying, before flaming me. Tips would be helpful, and so would suggestions on how to rape Mayans. The flaming, "YOU'RE A MORON" are not, and well... Just at least say why and say that.
Thanks for reading, and I hoped I sparked some thought.
-Ivan Antonov