A 30.06, regardless of the bullet used would not likely be considered "fur friendly". FMJs are non-expanding, therefore they typically pierce a small wound channel through the animal, causing questionable damage and blood trails. Like Jack said above, if you use them you will get all the tracking practice you could want, and even so would fail to recover many shot animals. Simply put, FMJs were not designed for the job you are considering them for, regardless of caliber or bullet weight. As was mentioned earlier, the animal deserves better than to escape and endure a slow and painful death. For not much more money than FMJs cost, you can find factory ammunition that employs bullets that are constructed to ensure quick, humane kills. In your search, you might even find a factory load that is more fur friendly than what you are presently using. If you handload, your options are far broader. If you are serious about saving fur, you may want to opt for a lighter caliber rifle altogether. Any of the .22 to .24 caliber centerfires are very effective on coyotes, and with the right load are fur friendly.