Having similar problems this year in our chicken coop. My old pump-up Benjamin pellet pistol gave up the ghost so I bought a C02 pistol/rifle (Diana Chaser) with a red-dot holographic sight and a "tactical" flashlight under the barrel. In the past eight evenings (two trips to the barn to "sweep" the area) I have shot 15 rats. Ours are roof rats. Since the beginning of the year I have also placed a Have-a-hart in the coop with the chickens (six trapped there) and unbaited Victor snap traps along the barn walls where the chickens (and dog) don't have access (11 killed in those). I also have placed Tomcat posion stations (yes, I hated to do that) which I loaded with an apple "flavored" block bait. The active ingredient is Bromethalin. I was VERY reluctant to use the posion as we have "volunteer" barn cats. Our are indoor bums . . . but that's fine.
I'm trying to remain careful with the bait blocks - the three stations I use are locked and I check the whole area every morning for carcasses BEFORE the dog goes out. The traps were basically ignored until I tried smearing peanutbutter on the blocks and a little dab at the enterance of each trap. Immediate success. So far I have removed 8 rats but I find "bits" where the survivors and mice have helped themselves to the easy protien. I open the barn and listen for the flies. They help pinpoint the deceased rats. All told 40 have been removed this year. Unknown how many are deceased in various tunnels and warrens under wood-piles, hay bales and behind equipment. There is definately the smell of death permeating the barn and attached coop.
The red-dot sight is not a night sight, and the rats skedaddle as soon as the flashlight goes on. So I pre-align as best as I can with the available light and click on the light with my left thumb. Rats "talk" and I have homed in on some by listening to their little "mews" and "meeps". Good sport as they seem very seldom to pause in indecision.
The target is five shots from 25 feet - good rat distance. And the supressor really does almost eliminate the sound. Without it the pistol is half as loud as a .22 LR +/-. With it there is just a little "sup" noise.