Your rebels cannot win a straight-up fight. So they won't give the enemy one!
An army in the field, especially an ancient army, cannot bring its own rations with it. It needs a continuous train of supplies, preferably by boat as grain transport via barge/ship is HUGELY more efficient than animal-pulled wagon trains. If the population is on your rebel's side, the easy answer is burn the fields, chase off the game, and have your rebel army act as a lure while whatever compromises your mobile force (preferably cavalry, but light infantry will work in a pinch if its forested/the enemy has few horsemen) attacks the enemy supply wagons. Disruption needn't take a long time. Stopping supplies for a week or two when there's no forage for the army could easily lead to serious problems resulting in the retreat/starvation of the superior force.
The enemy guards the caravans too well to be attacked. If this starts to happen it may weaken the main force enough for your "plucky rebels" to win the day in a fight with what remains of the army.
The Enemy Spreads Out In an attempt to keep fed off the land, the enemy army sends out foragers in small groups in all directions. This could lead to them finding sufficient food to bring your rebels to a decisive battle they can't win. On the other hand, it can also result in your rebels ambushing and annihilating these small foraging parties, especially if the locals are happy to point them out to your rebels!
The Locals Starve Burning the crops and hiding the food is all very well, but your locals NEED that food to survive. Destroy too much, fail to hide enough from enemy foraging parties, and the locals start starving to death. Starving peasants are much more likely to sell out your rebels than ones that have enough to eat. Politics only count for so much if your kid is dying of malnutrition. Not much to get around this, ancient war is HARD on peons. But perhaps if it's a fall campaign your rebels could work out a deal with some other power/polity to bring in foodstuffs after the enemy army is driven off. You could also try to feed them of captured supplies, but that's much tougher logistically than using it to simply feed your raiders/army.
As an aside, while your army may not be reliably supplied with food, they should have adequate water if the locals are on their side. If there is so little water they're having trouble even when they know where the water is, your problem gets much simpler. Poison the wells along the enemy's advance. It's not hard, just throw a dead sheep in and it's done. An army without water dies even faster than one without food, and the enemy will be compelled to either pull back or die.