Depends... If you're talking about the old style Foster slug and a smoothbore barrel accuracy and power will most likely limit you to about 40 yards or less. The old slugs were 1/5 ounce, something like 88 grains, nearly roundball in form, and at low velocity of less than 1,300 fps. I would suspect this will leave you a tracking job even with a good hit. I doubt you'd get a drop em' right there performance.
There actually have been some new advances in .410 slugs, the newest versions are heavier 1/4 ounce and at increased velocities of nearly 1,800 fps. Even at this power level you're still talking less than 80 yard effective ranges. Most likely the accuracy would be a bigger range limitation than power with the latest offerings.
I wouldn't get too excited about the .410 for a coyote getter. Not a real dynamic little number.