If weather is good enough for it, we hose each goat down, fill up a bucket with water & Permectrin II solution, and pour it over them, working it into their coat until they are saturated. That stuff works great. BUT, like most things <other than dust> it's not long lasting, so you do have to repeat treatment at least 2-3 more times. You need to dust their barn/bedding/etc.
We use the Permectrin based powder that they use in chicken pens. We also tend to dust our goats with that too opposed to the other kinds of powders - never had an issue, plus it seems to generally be cheaper too/get more in the bottle.
Once we think problem is under control, we use Cylence. We used it last winter with good success, and are trying it again. You put it down the back on the skin. They say 1cc per 25lbs. but the last few times we did that, it didn't seem to do much good, so we give them a little more.
If you try Cylence it CAN be very itchy the first day, but after that it shouldn't bother them.