Slitherine

Slinger units were common in this period and the Romans used then into AD times but they are not represented. Why?

Slings were a later invention really and woudl be better covered in Spartan, but they just never made it on to the unit list - I don't remember why.

Slingers were in general use throughout the region by somewhere between 600-1000 BC, although specific states may have used them in battle 500-1000 years earlier or possibly even before. Any earlier than that and they were probably considered as "hunting" weapons. The tribe of Benjamin was well noted for its hiring out of mercenary slingers, and the Biblical story of Goliath being killed by a slingstone dates the weapon back at least that far. Thrown rocks probably preceded it, which may have continued as a valid tactic for "auxiliary" troops long after it ceased to be a "significant" form of combat.

If added to CoW, it would have had to be a fairly late development for most factions (or else faction specific), by which time formed archers would already be available to most.