Killing birds does not solve the problem; it would not take long before another pair of birds moves in. Treating the cause of the problem, for example, installing bird spikes to ledges, guttering, window sills, rafters, beams etc will stop pigeons using your property making them unable to roost.
Poisons should never be used as non target species of birds and animals could be killed. Simply install the bird spikes and move the birds away from your property.
Dave B