Standard ACs won't work in that design and don't attempt to do something silly like turn an AC unit on its side. The best thing to do is to get a Portable AC (what I got last for the same kind of project). The trick here is just exactly how much space it's going to take vs the size of the window. You'll need something (piece of wood?) to keep force against the vent and to come up with a solution to the water that you're going to create (will drain from bottom of the unit). My installation was actually a sliding glass door, so I had to go so far as to build a small 'frame' that covers the gap above the venting. I'd previously had it going through a 'normal' window as well and needed less work for that.

The hardest part for the whole thing is the drain aspect as these units are inches off the ground (depends on the wheels) and the drain plug is maybe an inch above the bottom, so there's not much room for a drain pan and I hate that solution as it is because it creates standing water. It's not pretty, but I got some garden pavers, put them on top of a rug, put one of those car stands (the thing you roll it up onto, but without the ramp attached) on top of the pavers, and voila, elevated (but possible to tip over if pushed!) AC unit. I then used some screw-on PVC and a length of that clear rubbery hose-like PVC as a channel for the water to follow. I then created a passthrough drain path by drilling a hole into the vent kit. Now if I had this near a bathroom, then I could have done something like drain it into a walk-in shower, but that'd be a trip hazard.

Since water doesn't like to go uphill, I also rigged up a 5 gal water jug (the kind you normally buy for those water dispensers) with an inlet whole for the water to gravity drain into it near the top. To push the water Out (this is a manual process), I rigged one of those battery operated dispensers that you put into the mouth of the bottle, but connected another length of the clear PVC and routed it to my passthrough. Depending on the moisture levels, I think we had to drain it 1-2x / day.

We're still using this and the other window ac units in conjunction with a couple tower fans (in the hall) to distribute cool air through the house until we can FINALLY get central air replaced.