I have found that using a plastic mulch works well, or even re-purposing old tarps that I use to cover the hay works well. I also learned that they have to be dark colored to eliminate any light getting through, or else weeds will grow under them. I bought a new blue tarp to fit the area that I still needed to cover this spring, and I found that weeds grew under it. Black is best.
You can see the plastic mulch with the watermelon and other vine crops on the left, and the black tarp under the tomatoes, also the blue tarp under the peppers that didn't work to well.
Other years, I've used the large tarps as area for vine crops and that worked really well, as it's so hard to weed once the vines get growing. You can place a soaker hose under it to water, and that works well too.
Photo taken in about July of this year.