I and probably most use a chemical called 2,4-D specifically to eliminate willow trees. It is safe to use on/near water. I've found it works best new young trees or new growth up to around 6 or 7 feet. It seems to move the chemical down into the root system better in these cases. For larger full size trees, you can cut them down, let new growth start to shoot up to around 3 or 4 feet and then apply. You may need to apply twice withing a 2 week period. I only have one stump from a large tree that has sprouted back so far from earlier treatment this year. Thats out of about 20 or so young new trees and about 10 larger cut trees treated as mentioned.

Once you have them you will probably have to treat for them each year or every other year.

Good Luck!

John