Im on mobile, but what year is it? If its the old style belt tensioner, just stand off to the side while its running and tighten/loosen the belt untill the squeeling is barely noticeable, then drive it for a day. Think of it as a day of heat treating the belt. It will stretch and shrink to the magical perfect tightness on its own once your close...or atleast it has for me
.....or it could be a pulley, but generally speaking if it just started doing it after it being off, it just needs adjustment

 

OK guys I fricken fixed it and this is how. I tightened the serp. belt....pretty damn tight like everyone was tellin me to do... the squeal didnt stop. So I sprayed some lubricant on the pullies and on the belt and took it for a good drive well basically in some areas pedal to the medal and it stopped. I hope this helps everyone else with the same problem. My Jeep is an 89 jeep cherokee and if you are messing with the serp. belt make sure that on the late model cherokee's that they are tight clean and have some lub. as well as what everyone else has recommended... thanks so much to everyone that has helped cause this was very embarrassing for a guy that is a PROUD owner of a JEEP.

 

I learned this the hard way as well. I had gotten some coolant on the belt when my bypass tube rusted out. After I replaced it, my alternator would drop out at night when my lights were on for a few minutes. I was so pissed thinking that my 2 week old alternator had taken a dump. I remember hearing chirping sounds when the needle would plummet, like a slipping belt. Cleaned and tightened the belt a bit more and its been fine ever since. So, clean and tight is the rule of thumb for these belts.