As far as Maya unique units go, I hope it's not a bowman of some sort.
Most Mayan warfare was done at close-quarters with melee weapons often made of chert or obsidian, like the
Macahuitl. I suspect part of the reason for this is that the Maya jungles didn't make it easy to get uninterrupted projectile fire.
But the coolest unique Maya unit would be a unit
hurling wasp or bee bombs into the enemy (link to Google Books version of
Six-Legged Soldiers: Using Insects as Weapons of War by Jeffrey A, Lockwood, published by Oxford University Press). Basically the Maya would seal gourds with wasps or bees, shake them up to anger the bees/wasps inside, then hurl them into the enemy. This weapon came about by 2600 BC.
Apparently, the Popul Vuh (the Maya religious text about the creation of the universe) tells of traps using bee-infested dummy soldiers too, per Mr. Lockwood's book: