Getting rid of Buzzards

You could let some hunters loose and see if they take down the buzzards frequently enough for your liking.

You could also have a squad of marksdwarves under orders to patrol the area where the buzzards congregate, but I think you'll have to issue kill orders manually in order to kill the buzzards (best done from the list instead of selecting with the cursor).

You could chain up some dogs in the problem areas and they will scare away or at least fight most wildlife pests. They also make handy kobold/elf/goblin detectors so it's not a bad idea to do this anyway.

If you're truly desperate, you can edit your raws so that they have no brains and die instantly on spawning. In your save folder go to /raws/objects/creature_birds_new.txt and find the line that says [BODY:HUMANOID_ARMLESS_NECK:2WINGS:2EYES:2LUNGS:HEART:GUTS:ORGANS:GIZZARD:HUMANOID_JOINTS:THROAT:NECK:SPINE:BRAIN:SKULL:4TOES:BEAK:TONGUE:RIBCAGE]. Remove the :BRAIN: part and see if that helps. I would recommend making a backup of your save files before doing this.

Hunter dwarves will automatically try to kill anything that is edible, including animals other than buzzards. If your wilderness doesn't include dangerous animals, hunters should solve your problem nicely, as long as you keep them supplied with bolts.