try this

Here is a link that might be useful: plants known to grow under bw tree

hey - dont be bashing black walnut trees - they are beautiful... but of course beauty is in the eye of the beholder...

umm, StephenB, that description did not fit our black walnut trees. Maybe it depends on the climate.

I very successfully grew many bearded iris, vinca minor, MaDonna lily, and a Van 'something' sweet cherry tree under a perfectly huge black walnut tree, and hollyhocks under the other. The hh and cherry were out at the dripline and got nearly full sun. There was about a foot of old fallen walnuts I had to dig through to reach any dirt, I didn't bother to remove any of them.
GH

Thanks for the responses. I actually have become sorta fond of my BWT's. Grant you if I was building a new home they would not be something I would probably choose due to some of the problems you talk about. But since I inherited them ( about 9 in my back yard) I have made the best of it. I actually like their high dappled shade, and think they are quite pretty,the leaves have a nice tropical look. They are the last to leaf out and the first to drop leaves, but that allows extra sun for my spring bulbs and extra sun for my Japenese maples. The walnuts are messy though and some years produce more than others, but we are used to this fall ritual of picking them up.
I have many nice plants growing under them and they all do well.(hostas, bleeding heart,huechera,astilbes, lilies,ferns and many more.) But again I wasn't sure about any of the plants for sun d/t most of my gardening as been in the shade. I have checked out the links(Thanks Jopyeweed)but not all the plants I have chosen for sun are listed either way. I was hoping someone who has actually tried these plants could offer some of their experiences.
Walnut

Forget about the lavendar and sage. These are too toxic prone and lavendar is a short lived plant anyway. Your daisies and cone flowers and black-eyed susans will do just fine. So will daylilies and probably lilies. I know for sure that siberian iris will grow. But try the bearded ones too.

If you have tested the soil RECENTLY with tomato plants then you don't have a problem with the toxin. However, roots grow; so I would test again if you want to plant sensitive plants in that spot.

As for my roses, they all gave a good spring flush but have not grown much since then and have had very sparse rebloom. However, they also don't get a lot of sun. I'm inclined to think that is the cause of sparse bloom. They are otherwise healthy, except one--Daybreak. It died last winter. There were a number of roots invading its space.

As to whether or not to get rid of the trees, there are enough plants that will grow within the root zone of these trees to make them worth keeping. On the other hand, as StephenB says, they are messy plants. At least mine are. If your space is small, they certainly would not be my choice for home landscapes. Because they are messy, they require constant cleanup-leaves, branches, stems and the nuts, well there are times one cannot walk on that side of the yard because there are so many nuts. It is a hazard; the nuts are very slippery and if one should fall on your head--OUCH. They also stain-walnut stain was once made from the hulls. In the end it is a highly personal decision as to whether to keep or not. I keep because my neighbors have them growing along my property line so there would be very little difference in the toxin levels. The toxin also stays in the soil at least 5 years after the tree is gone due to decaying roots.

Hawkeye Belle,
Thanks for the response. I have already planted the sage and lavender ,but will remove it from that bed tomorrow. I planted a week ago or so, so hopefully they will be ok and will survive if moved to another area of the yard away from the BWT.I am glad to hear some of my other plants should do OK. I think next time I try a new plant I will make sure to establish it somewhere else first . Then I can plant divisions in the bed with concerns. That way if it should die at least I haven't lost the entire plant.
And you are right , They are messy and I have had my fair share of klunks to the head from falling walnuts.Thanks for sharing your observations of the roses. Sounds promising if hey have enough sun.
Thanks Walnut