The most commonly suggested control for buttercups is a broadleaf herbicide containing 2,4-D.
One of my farm friends told me that the application of lime to the soil will prevent buttercups. I don't know if it will kill them once they are established. She showed me two of her fields--one that had been treated with lime (no buttercups) and one that had not been treated (lots of buttercups). It also helps to mow them before they go to seed.