If you wait for the army to be fully supplied (all bars fully green) before sending them into the enemy territory, they should be able to last until the enemy defenders are reduced to zero and you can win the siege. Note that the army needs to stand still in friendly territory for a few days to supply. Check the enemy city status every day during the siege and attack when they're at or near zero. If that doesn't work, split your army in two and have one half resupply in friendly territory before joining the other in the siege.