Hi Gina,
I had a row of raspberries and a row of black berries in the middle of grass that did quite well. But I did weed them for a while. The cardboard or newspapers covered in woodchips worked well for me.
One of the issues I think is that raspberries and grass both have fairly shallow roots that compete. Depending on the type of grass, you might be able to build a raised bed that would help. Or if the grass wasn't too aggressive, you might be able to surround the raspberry bed with some kind of barrier like bricks or metal to try and stop the rhizomes from coming through. But a lot of grasses are so aggressive that wouldn't work.
