Teresa
@bluegrassmom I noticed in your picture you have iris in rows. My question is, how wide are your rows??? If they're wide enough, you could fit a push mower in there and mow down the grass and weeds on the lowest guard. Then lay grass clippings on top. However you will still have to hand pull weeds that grow very close to/in between each iris plant.
I have found this method very efficient when it came to my vegetable garden.