What are some quick possible fixes for a rough idle on a 96 jeep grand cherokee?

first step is swap out the plugs wires cap and rotor next is listen for vacuum leaks and repair

if that doesn't fix it you probably will spend more swapping parts than just getting it diagnosed rite and fixing the real problem

Hmmm hard to say, but let's ask more questions, idles fine in neutral or park but not in drive, Vacuum leak would be the simplest to eliminate. While, idling take a can of carb or choke cleaner and spray your vacuum lines at various places listening for a change in RPM. The idea is that if you have a leak or broken or damaged vacuum line it will suck in the choke cleaner and you will hear a change in the rpm. You can also "t" a vacuum guage in various places to make sure your vacuum seems good. With this out of the way, we move too looking at the plugs, put in drive let run for a bit (if you have to put your foot on the gas an break thats fine) 2 or 3 mins. Then shut off and pull plugs, inspect plug for lean or rich burning condition, or a possible wet plug, which would be no burn at all. If rich, too much fuel, got to sensors and ecu, injectors etc., If lean, go to 02 sensor. If wet, go to spark. So once you figure which way to go (lean or rich fuel) or (good or poor spark) you might as well throw in a compression test just to rule out the air aspect (air, fuel, spark 3 things you need for proper running engine) Compression should be about 150-200 within 10 percent of eachother across all cyliners. If you have this then you have to work on spark and fuel. Off hand, running rough at idle, sounds like a fuel issue, your either getting to much or to little, the computer sends fuel (opens injectors) according to sensor signals,(o2, map, mas, mat, coolant temp, tps, cps, etc..) at this point, pull codes in memory for a faulty area, and then figure out which sensor is supplying bad info to the computer. If you have a problem when warm but not cold, or when you first start it and you haven't replaced the 02 in 50-60k miles consider a new 02 sensor (only good for about 60k) otherwise good luck.

Have the vehicle scanned for codes and also have the data list information looked at. These tests will tell you if you have a simple motor miss, O2 sensors not working properly, a MAF sensor problem , etc.

A vacuum leak at the intake manifold wouldn't surprise me either, it's a jeep, the exhaust manifolds warp and loosen up and the same bolts/studs hold the intake manifold. A dealer will know the common problems.

Yes, the idle air motor is in the throttle body, but you are asking about a relay? The older Cherokees had what is called a "latch relay", this allowed the computer to stay on long enough to 'park' the idle air motor in the best starting position stored in memory. The later cherokees don't have that but they do have an "ASD"(auto shut down) relay. I'm not sure if they do the same thing, but this might be what you are looking for. It is in the black fuse box under the hood and labeled "ASD"

Hard to say, could be as simple as an open vacuum line, or could be a clogged fuel filter. There should be a sticker under the hood that shows a diagram of the vacuum lines, the fuel filter is underneath, somewhere along the frame.

Look on the intake beside the throttle body, There should be a plug in connector with three wires to it. That's your throttle positioning sensor try replacing that, And all your vac-um lines as well!

Have you thought about the checking the IAC and TPS?

Google it. You can test them with a multimeter.

The exhaust manifold is also very prone to cracking.

replace fuel filter & add a can of 24k to fuel tank. this is a product made by BG & is usally only found at repair shops &dealers so call around

It could be running lean for some reason. Maybe its an oxygen sensor.

check all vacuum hoses. spray some starting fluid around all fittings when the engine is cool. it will let you know when you find a bad hose. even spray around the intake gasket.