Trying to figure out what options really exist in terms of A/C for a coop apartment other than window units or through the wall units.
The coop does allow through-the-wall installations but does not look to be allowing anything hanging on outside walls.
Does anyone have any thoughts? Are there any ductless units where the compressor can be installed in a through-the-wall sleeve?

See http://streeteasy.com/nyc/sale/686463-coop-750-park-avenue-lenox-hill-new-york, where the LR has a regular ductless unit. The compressor may be out on the terrace.

The BR has an evaporator in an adjoining laundry room (i.e., where there's power and a drain) and the compressor may also be out on a terrace.

I think they were done that way because there's very little height under the windows for regular through-wall setups.

If you can finagle through-wall, just go with that. It's possible to have compressors through-wall and the evaporators elsewhere, but the refrigerant/drain/power linesets are pretty clunky and hard to hide.

Aesthetically, everybody's used to seeing through-wall cabinetry, while a mini-split evaporator up on the wall tends to be obtrusive.

Oops, they're balconies, not terraces.

Yes, split units NWT is referring too are pretty but your coop doesn't allow anything hanging on outside walls. I think that's pretty much it in your case, through the wall or window unit. What kind of windows you have?

Most of the windows are about 40'' wide

Here's another ductless system, with big ugly air handlers hanging on the walls. Compressors are out on the terrace behind latticework. http://streeteasy.com/nyc/sale/688406-coop-1215-fifth-avenue-upper-carnegie-hill-new-york

Looks that we'll be going with through-the-wall after all. Thanks, NWT and Arx.

I have a "mini split system" installed in my apartment, with both the evaporator/condenser unit inside and the air handlers. We replaced a window with a storm louver and placed the condenser in a small closet created behind the window. Fresh air comes in through an AC grill below the window, warm exhaust air goes out the storm louver / window. The refrigerant lines run to 4 zones within our apartment. I was skeptical at first, but the solution is awesome.

Earo

You solution seems to be pretty interesting. Would you mind posting some pics? I am having the same issue. The board at our coop would not allow the installation of mini split AC even after u tried to convince them that there would be no issues with it. Old people at the board have no idea how this thing is working and seem to be not interested to know. But anyway you solution might work for us. It just I am having hard time visualizing how you did it. Also on what floor do you live? How high? Thanks in advance.

I got a Daikin mini-split in my kitchen, ducting through the wall to the condenser on the terrace. Quiet and fabulous. In Asia, all you see are these units. Meanwhile in my other rooms I have P-TAKs which suck! Any suggestions on replacing?