There are a couple of things you can try.
See if you can get alliances with other realms or even major vassals in other realms that you can call into the war.
Otherwise, get some good commanders. Find the martial with the absolutely highest stat you can, and put him on train troops in advance. You can get a significant boost from that, especially if you have multiple baronies in your capital county. Ideally, you also get the +50% reinforcement rate so they fill/refill quicker.
If you know when the war is coming, especially if it is something you can trigger (like an arrest/revocation), raise your levies and gather your forces before triggering it. Put them in place so when the war is declared he won't raise his forces and the sieges start immediately. Alternately, use your already gathered troops and a commander with Organizer to kill his armies before he can gather them together. If you have retinues you can use them to adjust your troop mixes. It is quite possible to beat significantly larger armies with good commanders, especially if you can make them fight you when you are getting bonuses from the terrain and they are taking penalities for it.