Answer: The best time is in fall or late winter when they are dormant. However, you could do it now if you get as much soil as is practical, disturbing the roots as little as possible. Plant them immediately after digging. Make sure and water them in well after planting. Then keep them moist for the next few months to get them off to a good start.
Since black raspberries are not the most vigorous of brambles, I would suggest you set them at a spacing of 3 to 4 feed apart down the row. They do not need a support. Check out the following publication for information on how to prune them into a good hedgerow:
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