The tensioner is a consumable part. When you replace the belt you also replace the belt tensioner. You will need a mechanic's stethoscope to isolate the noise to determine which bearing is giving you a problem. As often as I replace alternators I would suspect that part first, but if it was a high mileage car with the usual lack of preventive maintenance as well as routine maintenance performed on the vehicle it could be just about anything.
It's likely the tensioner. However, double check like Dave said. Just use a long ratchet extension, or a piece of broom handle, place it on each part (NOT THE SPINNING PART!) and put the handle on your ear. You'll hear bad bearings immediately.
#2 is the tensioner, note that #4 shows an AC delete pulley instead of your AC compressor.
It may, but check the tensioner first. The compressor engagement may just be putting more load on the bad tensioner bearings. You might be able to tell be simply slipping the belt off the tensioner (like in pic 1) then spinning the pulley on the tensioner. It should be very smooth, no noise.