I think the dump probably has an area for what they call "white goods". Old appliances and such. I think an air con would fall into that category. Give them a call.
Ummm......having made many trips to the Miles City Landfill, I'm pretty sure you can....especially if you have several big lawn and leaf bags full of yard wastes you can pitch on top of the item in question.
If not, there are many accessible coulees to be found downslope of the Sheffield Road.
The landfill takes them, but you have to pay a fee because of the freon. Even if the freon has been let out. They pay a guy to come and remove the freon from each unit.
It has been a while but i think the fee is something like 10.00