rats, IMHO, are the common denominator by which every aspect of my coop is built.  keep out the rats and you keep our all else.  the main solution is using hardware cloth, which really should be called the true chicken wire.  the entire coop is enveloped in it, two feet down into the ground.  there is not a hole anywhere that an adult rat can get it's head through.  you will always have a few rats lingering around, that's no biggy, it's when the females get unfettered access to food that you can have a rat explosion which can really go badly for a variety of reasons.  if you don't want to go the hardware cloth route or can't right away, then make sure that the chicken food is not accessible at night, metal cans for storage and perhaps only feed what the chickens can eat each day.  out in nature the population is kept in check by predators and a limited food supply whereas in the coop, there are no predators and an unlimited supply of food.  two rats can become a thousand rats in just six months and they inevitably try and find a way in your house.  it happened to a friend, an exterminator pulled out over 100 rats from their basement walls... it was a disaster.  
poison doesn't work all that well and often takes unintended victims.  snap traps work well, the  black plastic kind are easiest to set and less intimidating all the way around.  I'd start with 10, bait with peanut butter mixed with chicken food and put them all over the place at night, closing the hens in their inner coop till you can remove them in the morning or place them outside where you know they get in to the coop.  hit them hard and consistently to get the population down before they start multiplying like rabbits and once you have them under control, go all out a couple of times a year with traps to try and keep them at bay.  if you get to the point where the rats know what the traps look like and won't take the bate, then I'd recommend taking a different approach where you stop using bait and instead use the traps as snares, placing them in spots where they run between hiding places.  it takes a little study of their nature but it works, if placed properly, the rats will run across the traps and get caught.  I don't mean to sound so intense about it, but I do recommend taking them seriously, and if you design well for them, you will virtually eliminate the chance of coons and other predators as well.