If you are patient, I suppose that goats could be used to graze the grasses back under control. Maybe you could smother the grass with used carpeting-though I can't imagine what an entire orchard would look like covered with carpet.

You would likely need to keep a close watch on goats in a berry patch. Goats are naturally browsers, and prefer twigs and brambles to grass.

Between the rows, some sort of weed barrier might work, especially if it was put down after a tilling. A thick mulch could do the same too. However if the grass has spread to in and around the berries themselves, it will be a much harder job. Hand weeding and mulches perhaps.

Goats prefer berries to grass so scratch that idea...
How large is the orchard? Pics?
I'm also thinking you may want to consider a weed barrier.