You know they are nesting, so they probably have eggs or chicks. We have a nest on our TV antenna, we are waiting till the babies fly. If you must, how about just cutting the branch they are on?
My husband did not like my idea for the two rousting over his truck.
He took a more permanent approach, waited until after dark as a plane flew past to cover the sound (not directly in the line of fire). One blast of the shot gun and all we had left was a shower of leaves, never even saw a feather.

Yea, remember the old cartoons with the X's over the eyes as the bird floats up into the clouds. We had a clear visual.