For the past few day, I have been using the Aeropress exclusively with coffee that are coursely ground. The grind consistency is almost as course as for French press, but a tad finer. On my Capresso Infinity grinder which I use almost exclusively for non-espresso brewing, the setting is on the fine end of the medium grind setting. The aeropress is shipped with instruction that recommend the user to use coffee of very fine grind (finess that is between espresso and drip filter) as well as numerous online Aeropress resources. And for the first week or so, I follow these recommendation about using such fine grind.
It kind of make sense for a brewing device like the aeropress to use finner grind. The paper filter that Aeropress uses is able to filter out fines of the coffee grounds; and finner grind enable shorter brewing time which the aeropress needs because of the rapid heat loss that the small volume of water in the Aeropress's chamber experience.
However, fine grind and short brew time in Aeropress has disadvantages. For instance, the coffee can be easily over-extracted if the barista is not paying close attention to the time or the pressure applied during the pressing phase is not consistent which result in too slow flow. When I started playing with courser grind and longer brewing time in the aeropress, I notice less bitterness in the coffee that it produces. I also notice more nuances of aromas and taste. However, it is critical that the aeropress's chamber is preheated with hot water before coffee ground are placed inside and brewed.
Give this a try!