In researching I found an excellent publication by Penn State's horticulture department that gives good information on this toxic substance and also includes a long list of plants that are juglone tolerant. Also, I found that there are several fruit trees that are tolerant and could be planted in the vicinity of a black walnut tree: “Cherry, Nectarine, Plum, Peach (Prunus), Quince (Cydonia oblongata).” (http://tinyurl.com/my2p8bj)
To the reader who posed the question, if you decide to plant apple trees again, plant them 50 to 80 feet from the trunk or stump of the tree (base this on the size of the tree's canopy when you cut it down). This is the area where you will find the roots of the tree, and most of them will be fairly close to the surface. When digging the new planting hole, if you run into a root, move several feet away so that the roots of the new tree will not come in contact with the root of the walnut. Fortunately the juglone doesn't leach very far from the root if at all.
Here is information that will hopefully help many readers deal with this situation:
•Do not add the leaves and other plant debris from the walnut or other types of nut trees to the compost pile.
•Although it does sound as if our reader's orchard suffered from juglone poisoning, symptoms of other situations can be similar, and it is worth asking for an evaluation from the Extension before cutting down trees. What may appear to be juglone toxicity might be something as simple as not enough sunlight. Most of our trees require full sun (six to eight hours a day), and the canopy of a very large walnut tree can be dense and create too much shade, which would cause trees and plants nearby to struggle.
•Large trees of any kind use up the moisture and nutrients in the soil and can easily deplete it for other smaller trees and plants that are in close proximity. Symptoms that are similar would be yellowing leaves, major leaf drop, obviously not thriving and often being attacked by pests, and eventually dying.
•If planting a vegetable garden, locate it well away from black walnuts and other trees containing juglone. Having said that, there are vegetables that are tolerant such as most root vegetables and those in the Cucurbita spp (squash) family.
•For plants that cannot tolerate juglone and will die quickly (popular home-grown veggies such as tomatoes, peppers, eggplant and potatoes) plant as far as possible away from an actual tree, and in good soil in deep raised beds — and whether the tree is gone or not, line the bed to protect these plants from coming in contact with the roots.
•Some ornamental favorites that are also very susceptible are petunias, azalea, viburnums, hydrangea and rhododendron.