Anybody that has done off roading or wants to do off roading in their Eagle has probably looked for options for tires and has been thoroughly disappointed. There is not much available for all terrains or mud terrains in the sizing that fits on an Eagle, and the options that are out there are quite pricey. I did find though that UTV tires will work on an Eagle. Be sure to check the load rating to make sure they can support the weight of the Eagle. Lots of these are also not DOT approved, so they will need to be trail only tires. The DOT approved ones will wear out quickly as well, so they probably are not a great daily driving tire. I have ones that aren't DOT approved, so they don't see the roads, but they do give a ton of traction off road, as can be seen in the video below. They do look goofy on Eagles.
These tires can be cheap too. I found a set brand new on marketplace in the 27x8.50R15 size and got them for $350
Here's a link to good pictures, its about the middle of page 9:
https://comancheclub.com/topic/66355-1986-amc-eagle/page/9/#commentshttps://www.youtube.com/watch?v=JtXmaTXVCtA