I just had the serpentine belt replace on my 1999 Cherokee. It now squeals periodically. Sometimes not so bad, sometimes really loud. I've doused it with spray-on dressing, which seems to help for a while.

Any suggestions as to what has caused this, or what may be going out.

Cause: Insufficient belt tension.
Remedy: tighten belt.

I have the same condition. I changed drive belt about a week ago. Cherokee does not have automatic tension adjuster, so you (or mechanic) have to adjust it once in a while. It is important specially the first few weeks after you change it. It should be fine after a couple adjustments, but it is important to check belt tension and its condition, once in a while. Also make sure you have it routed right. If it is done incorrectly it may spin water pump in wrong direction and overheat engine. Also don’t put to much tension on that belt. It could damage bearings in alternator, or other accessories. Adjust it gradually little bit at the time until it stops squeak. It puts more load on belt if you turn a/c compressor on, and may squeak more. If you are not sure take it to the mechanic, they have special tension meters, and they can adjust in no time So good luck, and keep you hands away from the cooling fan when you work on it.
Chris

could also be the belt it self! cheaper belts seem to make noise on cherokees.

My 1988 XJ 4.0 had a similar squeal, which was always minimized temporarily with silicone spray, and this is how I came to the solution:
I replaced the belt, adjusted it with a deflection gauge and still had a squeal.
I replaced the idler pulley assembly and it still squealed.
I decided that the problem was the fan clutch, so I removed the belt and fan shroud and, as I began to remove the fan clutch nuts, discovered that the water pump shaft was totally wobbley.
The car was not overheating or losing coolant, but the water pump bearings were shot.
I hope this helps...
Dale

My belt squealed really bad after I had it changed. I got out my sockets and a wrench and adjusted it. It no longer squeals.

I had a similar sounding problem, turned out to be the ac pump clutch. It was impossible to find until the bearings in the clutch totally went out though.