I have had to get mildew off wood before and I used a mixture of bleach & water (1/2 and 1/2). You will have to rinse with clear water after washing with the bleach mixture, but it should clean the mildew off and it won't come back very quickly at all. Mine lasted years.
Try 1 cup ammonia, 1/2 cup vinegar, 1/4 cup baking soda & 1 gallon water - Try a spray bottle to get it onto the ceiling. Will need to rinse!
I have the same problem and was wondering how to tackle it. I heard that oxyclean and water. Rinse after. But I have not gotten to it yet, so any info is greatly appreciated.