How can I plug a hole cut in a window pane for a portable A/C unit?
I highly suggest what I would call the 'board up method' I've seen in places, but executed classier of course. I would create two rounds (squares would also work) roughly an inch larger than the diameter of your hole. I would suggest some nice 1/4" plywood or similar. Then drill a hold in the center of both pieces and use a bolt and nylon locking nut of sufficient diameter to pass through the bits you've cut + the thickness of the glass.

Then with a little help from a friend or a particularly sticky piece of tape, have one round on the outside of the glass, one on the inside and both through the holes of the cut pieces and gently tighten the bolt.

Then you end up with not a plug so much as what I'd call a "cap". Pieces of felt, cloth or similar would help keep the pieces sealed to the window and prevent any scratching.

These rounds could then be painted to be less obvious and help prevent them from weathering in the even that they were rained on from the outside.