If there are no other plants besides the trees and the trees bark is intact try this:
Use your weed wacker to cut up the edges of the ivy. Nothing fancy, just make some cuts. then spray with Roundup. The cutting lets the Roundup penetrate the cells of the ivy leaves. You may have to do this two or three times-it just depends on how well you cut the ivy edges and sprayed the Roundup. Don't do this on a breezy day as the Roundup will kill all vegetation it touches.