I don't know about cherry trees. I do have oak trees in the yard, and I have never had a problem with a chicken eating an acorn and dying. I can't say I have actually seen them eat one either. Three of my coops are under Chinaberry trees. I was very worried about this when I found out they...
My small yard coop sits under 2 china berry trees for shade. I have never lost a chicken to anything but a predator. My 3 year old kept feeding them the leaves through the side of their pen before they were big enough to let out. I explained to him why he should not do that, but he kept it up...