Warriors and archers do fine (as long as you use good defensive terrain). By the time zombies are tough enough to give them problems, you can upgrade to swordsman and crossbows. My culture games don't last long enough to need to go past those
30 in marathon mode. Through most of ancient era, I was killing a zombie every 3 turns or so, along with other miscellaneous barbarians (I would raid a camp and then disperse it), rinse and repeat as new camps showed up. I might have only had a base 4 cpt from my capito, but I was generating 15 cpt from barb and zombie killing.
Marathon speed is the key as the culture gain from kills is tripled, but things to kill are spawning as if it's normal speed.