When I was a kid I used to make the whistles out of the willows that you find near the lakes and rivers. I tried Dogwood, willows, birch, and poplar saplings (bitter!). I found that the best season is in middle to late spring, only because of the amount of water in the stems.
Cut a length of sapling then form the whistle with notch on the top. Be sure to leave a section for you to hold while you are tapping to loosen the bark from the wood. Then cut the bark around the base of the whistle. Gently tap the bark, all the way around the stem. Generally I find that when the water oozes out of the ends that the loosening step is at hand. Grip the bark and twist slowly, the bark should loosen and slide off. Form the inside of the whistle and moisten the wood before sliding the bark back on. Then blow! Adjust shrill by opening the gap where the wind escapes the whistle.

Hope it works!