What is the easiest way to find out what gear ratio is in my 96 XJ without removing the differential cover?

Should be 3.55's. Not sure if there should be tags on the diff covers or not.

You could just get a build sheet on your vehicle:
http://www.jeep.com/webselfservice/jeep/EmailPage.html

I second getting the build sheet, its just a neat thing to have.
I submitted a request for my XJ's and got it two days later after the weekend. I submitted one for a WJ and had it later that Saturday.

quick and easy

Manual 4.0, probably 3.07. Auto 4.0, probably 3.55.