Whatever birds will eat them, put out a lot of birdhouses for them.
We have one little crew o family of bluish grey feathers with slightly black crest that unfortunately nest on one of our fans on the east porch, they sit n the railings and nearby trees and catch every bug that comes into the area. Don't know if they cthc stink bugs or not. And we have three families of crows that patrol the yard/field every day several times a day catching bugs plus the turkeys, If someone knows what birds eat them then tell us.We have a few stink bugs but no many. I will definatly build bird houses for any birds that will eat them. I had understood not many birds would.