Get an Owl, SERIOUSLY, we have a silhouette of an Owl with staring eyes on our garage roof, keeps the pigeons out a treat and the smaller birds seem to ignore it. (you can get them in garden centers)
If their droppings were explosive, my patio would look like an aerial photograph of the Somme in 1916. I hate to think how much time and water I spend each week in summer hosing off their ordnance. What is it about my neighbour's tree that attracts squadrons of the beggars?