My two dogs have similar acreage. I have a plastic container that I bought at Family Dollar. I take that in my left hand and in my right hand I hold a set of 12-inch metal "tweezers" (for lack of a better term), and every day I go around the lawn and pick up the droppings. After the container is full I take it to one spot in the woods and dump it. Possums and other critters take care of it from there.
For those of us with 1 acre or less, just use a garden hosepooh turns to poof!