I’ve had great luck with a mixture of high-concentrate vinegar, a little dish soap, and some salt. It absolutely puts Roundup to shame. This mix is non-selective though so be careful around the plants/grass you want to keep.

Using this mix with a battery-powered backpack sprayer is AWESOME.

Edit: Make sure you rinse the sprayer real well afterwards though, vinegar and salt aren’t great for the seals/pump.