About 5 in 10 games, I play against Byzantine opponents, who seems to be able to counter virtually almost everything, especially with their UU and cheap trash units.
How can I counter a Byzantine army of cataphracts, halberdiers, and skirmishers? Want to make infantry as Goths, or Aztecs? I get attacked by Cataphracts. Want to rescue my infantry from Cataphract attack with cavalry, or playing as a cav civ like Persians, or Tatars? Halberdiers wreck them, especially in cheap numbers!! And if I am an archer civ, or wanting to send archers to try countering the infantry and at least, Cataphracts? Skirmishers also wreck them.
Apparently my mixed army comp of cavs, archers, and infantry could get bagged by a Byzantine Army. I remembered playing as Britons long ago, and I lost my longbowmen and cavaliers to the Byzantine player!
As one that played Goths, Saracens, Turks, Tatars, and Lithuanians, I’d get done in by Byzantines.
There’s no rule saying you just have to make 1 unit, you can also make a mixed army comp. Siege might also be a nice addition to kill skirms/halbs. Heavy cav and an archer unit could be an option off the top of my head, the cav kills skirms/Catas, and ranged units or siege can deal with halbs maybe.
Byz has below average siege units and weak stable units so I think you can beat them with stronger siege units. Another civ that can destroy Byzantine is Sicilian with their cavaliers + skirm / arb as they really don’t have any answer to that Sicilian’s combo.
You are planning to counter the counter civ, which really doesn’t work much. As Hera said, double gold unit compositions are your best friend, particularly Knight + Crossbowmen type. Cataphracts die to both of these, Knights in front do not take any bonus damage from Skirmishers, and your crossbowmen behind can cleanup enemy pikes which are attacking your knights. Eventually you will need to refresh your Knights, but not Crossbowmen (if you play correctly).
Your asking the wrong question Byzantines are the king of cost effective trades, by try to counter their army head on you are playing into their hands If you have a good eco bonus, just play defensive. They are a defense and counter not a booming and offensive civ. Trash units are at bad at going offensive and if they make non trash units they are neglecting their civ bonus going on the only you have to worry about is towers. so make sure your access to your resource(s) can’t by easily be shut down by a couple towers or at the very least have a contingency plan.