They're not zombie overlords
They're zombie protectors.
First of all, no human citizen of this new country is required to serve in the military anymore. Maybe the old army was voluntary, maybe it was compulsory--regardless, it's something that can be pitched as a new kind of freedom. The zombies are here to shield us from the scheming, aggressive nations at our borders! The remaining soldiers can be disarmed and generously granted amnesty. They get to come home to their families! If they still want to take up a combat-oriented career, there are great opportunities for one or two humans to work alongside each zombie platoon, providing a friendly face as they patrol the border (and also dividing them up so they don't have opportunities to coordinate armed resistance).
They're not just protectors
They're a zombie labor force.
Every large society requires tremendous amounts of human labor to function--agricultural work, mining, building, transportation, and (beyond a certain point) dangerous, low-skill industry. If zombies are capable enough to defeat an army, they're capable enough to swing a pick, or pull a plow and pick weeds. "A Zombie In Every Shed" is a reasonable propaganda slogan, especially if it gives everyone more leisure time.
Sure, there is the slight price that families won't be able to bury their own dead anymore. But as long as Grandpa gets shipped off to another part of the country where the family can forget that he's been sentenced to endless labor in undeath, people will get used to it.
They're not just a labor force
They're a zombie surveillance instrument.
Okay, this part is less suitable for propaganda, but depending on the nature of the necromancy in this world, the empress could very well use her well-distributed hordes to personally observe and gather information on any fomented rebellion, then quash it before it has a chance to gain momentum. Many people, even under occupation, are willing to accept peace over freedom if the rebellious never get a chance to disseminate and promote their ideas; if that peace also comes with an increased standard of living, it's a much easier sell. And the longer the era of peace, the more acceptable it becomes.
Won't the rebels just hold their meetings out of sight of zombies if they catch on? Sure, but zombies might become effectively invisible in a surprisingly short time. (Right now, in 2017, thousands of people are installing internet-connected microphones in their own homes because it's a convenient novelty.) If they're given shrouds to reduce the sight and smell of rotting, people will start to see them as furniture. It might even be a popular project for people in domestic roles to knit or quilt shrouds for their zombies.
The Overton Undead
So those are your policies: disarmament and amnesty for human soldiers; migration of the armed forces to the living dead; broad distribution of free labor to undesirable jobs; and instant, quiet suppression of insurgency. Humans probably will thrive, just like some animals in captivity. And if they fail to thrive--hey, more free zombies.