Glyphosphate - aka Roundup.
I normally do not like using chemicals in my garden, but I resorted to using Roundup to get rid of the horribly invasive blue dayflower (Commelina communis)
which was taking over my foundation bed. This plant roots at stem nodes wherever they touch the ground and it is also a heavy re-seeder.

Anyway, I used a small(ish) piece of cardboard to shield nearby desirable plants from the spray. There is also a setting on the bottle for foam, which makes it less likely that you will get any overspray on nearby plants. You may have to retreat a time or two, but the Roundup should do the trick. Remember to resist the urge to pull up any of the plants too soon after treatment - the product needs time to make it to the roots or it won't work.

HTH~
RENEE

Here is a link that might be useful: Glyphosphate/Roundup

Sounds like black medic... that's what I've been yanking out of my backyard. Luckily, I don't have much of it. I'm trying to encourage my clover. Goodluck!