Black walnut gives off juglone, which is a chemical that makes it hard for other plants to grow.
Unfortunately, a quick search indicates that there aren't any native grasses that are juglone resistant, e.g. Mr. Smarty Pants at wildflower.org. Zoysia might work, but it doesn't sound like that's a clear winner either, and it grows best in USDA zones 6-9, which is warmer than where you are.
That site lists some other ground covers that you may want to consider:
- Chasmanthium latifolium (Inland sea oats)
- Sedges like Carex blanda (eastern woodland sedge)
You could probably plant an attractive mix of these species underneath your black walnut.
If you're willing to consider something other than grass, Toby Hemenway suggests a walnut "guild" in "Gaia's Garden" on pages 194-195. Species that are suggested are elderberry, hackberry, wolfberry, mulberry, Eleaegnus. Currants, if grown with hackberry, may work under walnut. He also suggests the possibility of tomatoes and peppers, as well as legumes.