“I explained that I did not want any window air conditioners installed due the eyesore factor and possible need to attach supporting shelves to the house”
Tell her she can add a window air conditioner as long it is removed when she leaves with no damage, otherwise cost of removal and/or repair will be taken out of her deposit.
The eyesore factor is irrelevant if you are not living there, are not trying to sell the house and it is removed when tenant leaves. As long as tenant purchases a brand new window air conditioner, it should be small enough that a shelf support isn’t needed. I had a roommate buy a window air conditioner and helped him install it. It was fairly easy to do, the conditioner frame is build so that the window can close on top of it and the a/c is held in place by a part of it’s frame (flange) that rises up on the inside of the window and leans against the window frame. Tenant will need to secure the a/c to the window frame using screws (so that the window can’t be opened up which would result in the a/c falling out of the window), but those holes can be patched up afterwards with wood filler, liquid steel or other patching product.
If you are concerned about damage during installation, you can always add the condition that it be installed by a professional.
If I was willing to entertain the idea of tenant paying for installing central a/c then I’d have zero problem letting them install window a/c. In fact, I’d prefer the window air conditioner because the worst case scenario is minor damage to the window frame. Installing central air and expecting the tenant to pay for it sounds much, much messier.
P.S. the summer this year was pretty brutal. At our house is was over 100 in the house for several days and we live less than 10 miles from the coast. The only refuge for the a/c-less is to go to places like Starbucks or the mall. Our roommate moved out and left the window a/c so we also huddled in that room occasionally. Those high temperatures without a/c becomes a big inconvenience, it does become difficult to sleep or be productive at home. We are definitely getting a whole-house fan and are considering either installing additional window a/c units or central air.