Boris Gudenuf
Deity
I'm not an "optimal" player so take my opinion with a grain of salt, but my assessment would be that the Maya are better suited for defensive war than offensive.
Given that the Civ is designed to start losing steam once they get too far from their capital, unless they give Lady 6 Pack the option to move her capital, any offensive effort is gong to run out of steam.
Best defense against the Maya would be simply to fall back until you are 8 tiles away from their capital, then counterattack when they reach the 7th tile.
Or as us Russian Military History types might put it, the Mayan Military Motto will be: Never attack anybody with a Great General named Kutuzov.
Speaking of which, the old lag about "The best defense is a good offense" is pure Croc. Ask Napoleon, Hitler, or the American Confederacy, all of whom basically attacked themselves to death.
It is much better to remember that:
"A weapon is offensive or defensive depending on which end is pointed at You."
- Which applies especially to the Mayan UU: a good ranged unit can be used either offensively or defensively and will dominate in either mode if you know what you are doing. Protect them against Cavalry and shoot util you run out of targets . . .