The Assyrians are a good civilization for early rushes since their villager bonus can allow them to advance through the ages faster and scout the map faster than other civilizations.
The Assyrians can begin to flex their muscles as soon as they hit the Tool Age and build an Archery Range.
Their fast villagers allow to get ahead of other civilizations, both in research and resource gathering, so you can try to be the first to make it to a subsequent age, build a small army, and strike while you have a technology advantage.
The Assyrians also have excellent archers and will make up a large part of your army. It's not a bad idea to get a small group of archers together immediately after you get to the Tool Age and build an archery range.
Use them to harass and slow your enemy's resource gathering, picking off villagers and retreating when they come under fire.
With their fire rate increased, a large amount of them can wipe out an entire village within minutes. This makes the Assyrians an excellent choice in small land maps.