Just about anything with 2,4-D in it will work. In most places it's controlled, but you can buy it in one quart bottles without needing a license.
The trick is in the timing of when you spray. You want the weeds to be actively growing because that's when they are drawing the most nutrients into their growth. I've been told that it takes five years of spraying every Spring to get rid of everything. I've done it once and had good results, but then I keep the area mowed and that helps a lot too.
My wife is a Master Gardener and they don't like using chemicals if there are other methods that work. Their number one way to control weeds in a paster is regular mowing. I've found that it works too, but it takes longer to get there.
I had to buy a 70 hp cab tractor and 12 foot batwing to maintain my place. Before I was using a 37 hp open station tractor with a 6 foot cutter, and it was too slow to get it all done. The heat also kept me from mowing when I should of, but there is a limit to how much I'm willing to suffer just to mow a pasture. Now with the cab, I can mow during the worse heat of the day, and with the bigger cutter, I can get a lot more done in less time.