Are you setting the AF to a single point? In this situation I find it best to fix the AF to one point, normally the centre which is the most sensitive/accurate, and stick with that. There are a number of 'intelligent' AF tracking systems on the market but unfortunately they are fairly new and often fitted only to the highest spec cameras. Fixing the AF point means that you know which one is the one to keep on the subject and the camera is less likely to be confused by trying to decide for itself which point to use.

Even then a lot is down to technique and you will need to practice as much as possible to be able to keep the target squarely under the AF point. Focus hunting is not uncommon and usually happens if the target drifts from the AF point or light and contrast is poor - especially as the lens hasn't got the fastest aperture range. Most AF systems work best at maximum apertures of 5.6 or better so at f6.3 the aperture is probably on the limit of what the AF can handle. This is a big heavy lens and at a 35mm equivalence of up to 1000mm camera shake is a potential issue - possibly enough to blur edges sufficiently to reduce contrast and affect AF accuracy.