Now we know a bit more about Assyria. The Siege Tower gives a bonus to adjacent units. The Royal Libraries give XP when their Great Work of Lit slot is filled.
I would guess that the best strategy for them is to go Liberty to get a free Great Writer in order to get an early Great Work to slot in the Royal Library. So you want to bee line writing for that. Then you might want to begin bee lining mathematics to get your Siege Towers going as early as possible.
Presumably they are melee siege units like Battering Rams, so pick up Composite Bowmen to go with them.
Once you've got that going, start taking rivals' cities to help fill up your tech tree. Statue of Zeus would be helpful for Assyria, so build it or steal it while you can. And if one of the militaristic city-states has Ballistas, that would be a good unit to go with your siege towers.