Often the actual pane unit for awning and casement windows can be removed (especially in newer and higher end windows). If this is the case, you can install a standard window air conditioner.
You would use an "L" shaped bar, called angle "iron" or angle stock (actually aluminum is probably more convenient), placed at the top of the unit instead of the upper sash to hold the unit in the frame.
The flat inside face of the angle iron would overlap and be screwed into the frame at the edges. The horizontal edge of the angle would be trimmed to fit inside the frame.
The air conditioner can be centered in the gap and the AC units side filler panels can be used to cover the gap. In the alternative, filler panels (clear plexi or any other thin weatherproof material) can be cut to fill the rectangular gaps on either side of the unit in place of the AC unit's fillers, which usually do not seal too well. In the alternative, the unit can be centered and one panel used to fill the gap. Be sure to seal around the AC edges and around the panels in either case.
Because most awning windows are not too tall, you may need a low profile AC unit such as this one