I use just about any arrow for stump shooting. Right now I'm using woods and rather than using field points I've switched to blunts. A field point, because it is basically a cone will try to steer around a hard spot in a stump or log or whatever and the result is often a head broken off. Since I've switched to blunts I've not had this problem.
With carbons I just put a small flat washer (fender washer) behind the head and have at 'er. I will sometimes reinforce the tip end and nock end of the carbon with a short piece of aluminum shaft.