Insectivorous birds can provide ecological and economic services by decreasing pest populations in agricultural systems, but the magnitude of effect is often debated. We modeled the capacity for birds to suppress pest population growth using a common tropical coffee pest, the coffee berry borer (CBB) (Hypothenemus hampei) as a study system. Previous field experiments show that birds play a role in suppressing CBB infestations through predation, but the degree to which birds can suppress population growth enough to control infestations is unknown since CBB are only vulnerable to predators when gravid females disperse. Using previously published data on CBB life‐stage survivability, we constructed a female‐only, daily time‐step, deterministic Leslie matrix and projected CBB population growth for a single breeding season. Our goal was to assess the plausibility of CBB suppression by birds as a function of avian energy requirements, reported avian densities on coffee farms, prey composition of avian diets, estimated a caloric value of CBB, and the initial starting population size. Our model showed CBB population growth became exponential (λdaily = 1.042) and that at low, but not medium or high population sizes, were birds able to reduce population growth by 50%. In general, birds exert predation pressure on insect populations, but the ability to control infestations is complex, and is likely dependent on the initial CBB population size.