On the nest boxes, if there is no coop, something you might try is to drape a cloth of some type, burlap, etc, partially over the fronts. It will look like a dark place to hide their eggs.
If not a concrete floor, is something like brick paving stones or slate rock available? Something that moisture won't harm and rats can't tunnel or chew through. Rats are prone to making tunnels under the coops and popping up and out to harm chicks, steal feed, etc. A concrete floor is the best option to deter their progress, but as long as it works like a concrete floor, it should suffice.
Not sure what cloth would keep them from chewing through it. Kevlar maybe?