i used the gun method in the past for rats and it does not bring their numbers down (makes you feel good though, revenge is sweet). if you coop is not rat and mouse proof then there is nothing you can do. if you can pass your finger from the outside to the inside of the coop then any rat can get in.any hole larger than 1-2 cm (2/3 of an inch) is a door for rats. if you insist on the air gun method then i would suggest a large air gun . i have a 22 cal weirauh x theoben, 32 foot-pounds of force fitted with a night scope ,it works miracles with rats at night, but i think cats are far better than any air gun they work all night and they enjoy it .i have 4 cats, 2 of them are excellent rat killers (they are large 6+ kilos). rats live in my yard (they feed from the compost pile) but they never managed to enter the aviaries (they tried their best ). in a yard with 2 dogs and 4 cats rats live very short and scared lives and they do not go around allot , baby rats are almost all taken by the cats (i can tell when baby rats leave their nests ,they end up at my frond door as presents ).