My experience is nothing does well under a black walnut tree, but it could be for other reasons.

http://www.treeboss.net/juglone.htm

The list of possibilities for under your Walnut tree is:

Trees & Shrubs

*

black, red, sugar, Japanese maples (Acer spp.)
*

serviceberry (Amelanchier spp.)
*

river, cherry birch (Betula spp.)
*

eastern redbud (Cercis canadensis)
*

fringetree (Chionanthus spp.)
*

hawthorn (Crataegus spp.)
*

daphne (Daphne spp.)
*

forsythia (Forsythia spp.)
*

thornless honeylocust (Gleditsia triacanthos var. inermis)
*

Carolina silverbell (Halesia tetraptera)
*

witchhazel (Hamamelis spp.)
*

rose-of-Sharon (Hibiscus syriacus)
*

hydrangea (Hydrangea spp.)
*

American holly (Ilex opaca)
*

eastern red cedar (Juniperus virginiana)
*

sweetgum (Liquidambar styraciflua)
*

black gum (Nyssa sylvatica)
*

Virginia creeper (Parthenocissus quinquefolia)
*

mock-orange (Philadelphus coronarius)
*

oak (Quercus spp.)
*

black raspberry (Rubus occidentalis)
*

elderberry (Sambucus spp.)
*

lilacs (Syringa spp.)
*

arborvitae (Thuja spp.)
*

Canadian hemlock (Tsuga canadensis)
*

elm (Ulmus spp.)
*

some viburnums (Viburnum spp.)

Perennials

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bugleweed (Ajuga reptans)
*

hollyhock (Alcea rosea)
*

Jack-in-the-pulpit (Arisaema triphyllum)
*

European ginger (Asarum europaeum)
*

false spirea (Astilbe spp.)
*

bleeding heart (Dicentra spp.)
*

leopardsbane (Doronicum orientale)
*

crested wood fern (Dryopteris cristata)
*

trout lily (Erythronium americanum)
*

sweet woodruff (Galium odoratum)
*

perennial geranium (Geranium spp.)
*

Lenten Rose/Christmas Rose (Helleborus spp.)
*

common daylily (wild orange type) (Hemerocallis fulva)
*

hosta (Hosta ssp.)
*

Siberian iris (Iris siberica)
*

lily-turf (Liriope spp.)
*

lobelia (Lobelia spp.)
*

bee balm (Monarda spp.)
*

sensitive fern (Onoclea sensibilis)
*

cinnamon fern (Osmunda cinnamomea)
*

garden phlox (Phlox paniculata)
*

great Solomons seal (Polygonatum commutatum)
*

Christmas fern (Polystichum acrostichoides)
*

primrose (Primula spp.)
*

lungwort (Pulmonaria spp.)
*

bloodroot (Sanguinaria canadensis)
*

live-forever (Hylotelephium (Sedum) spectabile)
*

lambÂs ear (Stachys byzantina)
*

meadow rue (Thalictrum spp.)
*

spiderwort (Tradescantia virginiana)
*

trillium (Trillium spp.)
*

Canada violet (Viola canadensis)

Bulbs

*

glory of the snow (Chionodoxa lucilae)
*

spring-blooming crocus (Crocus spp.)
*

Spanish bluebells (Hyacinthoides hispanica)
*

winter aconite (Eranthis hyemalis)
*

snowdrop (Galanthus spp.)
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hyacinth (Hyacinthus orientalis)
*

grape hyacinth (Muscari botryoides)
*

daffodils (Narcissus)
*

Siberian squill (Scilla siberica)
*

tulip (Tulipa spp.)

Annuals

*

wax begonia (Begonia semperflorens)
*

pot marigold (Calendula officinalis)
*

morning glory (Ipomea purpurea)
*

pansy (Viola x wittrockiana)

Good luck!