Hi Beth:
I would say early September through early October is the best time to harvest nuts from black walnut -- just have to beat the squirrels !!!
Interestingly, this is one of the worst walnut 'nut' crops in east-central Illinois I've seen in my 20+ career. Black walnut tends to be a consistently good producer of nuts, but not this year in my part of Illinois...very odd!
Best of luck!