Stay away from the busy times, like the holidays. I think there is no real slow time any longer. What you have to do is plan your trips to the parks on the weekdays. Spend the weekends at your resort. Also, make sure you get to the parks at opening. That makes such a huge difference in the crowds.
So, if you like it warm (wearing shorts and tshirts, and not even packing jeans), then go for early Sept. You WILL have to leave in the early afternoon because of the heat, but that would be a good time to take a nap & swim. Head back to Epcot (or a late EMH park) around 5pm. The evenings are BEAUTIFUL in September. Still warm enough for shorts and no sweathshirt.
If you don't like the heat at all, then go for January. But be prepared to wear your winter coats and gloves in the evenings. Because it won't be blistering hot out, you will most likely be able to stay in the parks all day.
The one thing I noticed is when people talk about how uncrowded the parks are, it's usually because they are NOT there on a weekend, and they got to the park at opening.
HTH