How do I get the Invisible Exploding Fireball Arrows through console commands?
Checking the Creation Kit, there is an item with editor ID "dunJaphetsFollyCWCatapultAmmo" and item ID 961D6. So you can give yourself 10,000 of these arrows and equip them with these commands:
player.additem 961d6 10000
player.equipitem 961d6
The arrows are invisible except when they're in flight, and they have no name in the game, but they work. You can't see the arrows in your inventory, so you either have to carry no other arrows or use the console to equip them.
On the subject of unusual ammo types, you may also be interested in item ID 73FE6: "CWCatapultAmmo." It's like the Japhet's Folly ammo but spreads fire where it lands. My guess is that this ammo type is used for the catapults during the Civil War.
(I wasn't able to catch the arrows by getting hit with them during the quest. Perhaps the Unofficial Skyrim Patch prevents the arrows from entering your inventory when you're hit with them—I don't know.)