Although we are not organic certified, we use very little pesticides and no herbicides. The only reason that we use a pesticide is because recently an awful "coffee borer beetle" plague and soon after a"coffee rust" plague swept though our region, which had an devastating effect on the coffee. Many of the organic farms were forced to replant entire farms! In this case we did decide it was necessary, however we control the weeds by hand(instead of using herbicide), which means to go into the coffee field with either a machete or a weed eater and cut down the weeds. This is speaking of our own farm.
Even though we can't assure you that the farms that we buy from do the same, to our knowledge, they would also control the weeds the same way we do. The pesticides and herbicides are costly, so the farmers try to use as least as possible in order to keep their profit.