I am having decent results with my Pentax DA50-200mm. I am using center spot focus. Here in a minute when it goes completely covered, I do not know if the AF will work anymore.
Most digital camera autofocus relies on identifying sharp edges or thin lines, but not where something really bright (the moon) meets something really dark (the sky or space beyond). Sometimes the autofocus can home in on the facial features (as in the man in the moon), sometimes not.
In a fraction of a second, the shorter the better, the camera literally tries different focusings and spot-check-analyzes the sharpness of the image (here and there) and when it thinks it has the sharpness best, it snaps the picture.
Does your camera have an "infinity lock" setting, which should work well for such long distance shooting?
Strangely, the infinity setting does not bring the moon in to focus for me. I mean, how much farther away can it be? I did not exactly have the very best lens for the situation, but my focus and results were so so.
I shot RAW and have not had any chance to process them, but hope to tomorrow.