Jeff,
Where abouts in the US of A do you live? Sounds like you're out in the backwoods seeing how you're mentioning coyotes. If you're looking to put a coyote down with a 1077 you would be best to bring a friend with a more powerful airgun and work on "teamwork rythm(sp)" and fire at the same time at the head. I'm sure the 1077 can take out a something that large but it'll need a /LOT/ of head shots and /VERY/ pin-point specific shots like the eyes, ears (shot into the ear hoping the shot will enter the brain), and possibly a groin shot to slow the coyote down.
I'll be up front with you here, I have never hunted mid-sized game like that before. I consider myself a target shooter but I have shot a "prey/game" in my backyard before. To be more specific on the game I shot was crows, squirells (sp?) about the size of ones elbow to shoulder length, and birds smaller or equivelent to the size of crows. I would think to put a coyote down with a single shot on the 1077 is not impossible but I'd say the odds are 90% and higher for an animal of that size to go down without multiple or possiblely a "volley/hail" of shots landed into the above mentioned locations is very, very slim. But hey, there is always that one in a million shot there

Make sure you bring a Droidz or some high capacity auto or semi-auto gun with you if you have to run because the animal is charging you.
Mid-sized game like that is always an "extra" challenge and with the limited long-range capabilities of 1077 you would have improve on your camoflauge, tactics, positioning, and stealth. On the upside some of those skills can be transferred (sp?) later on in real-life when you're in the working world. Tho, in the working world the terms would be called "business strategy". I recommend you check up on a book called "The Art of War". Originally it was used as a manual for "war" in the ancient times if I recall correctly. Alternatively you can also check out the audio book version of it if you have can find it on the web. I've never owned the paperback copy but I've heard the audio book version. I take the teachings fromt he book and put them to "business/work" use then for the "war" use.
Gotta go now. Someone needs the computer here. BTW, how old are you? I hate to get all grammar/spelling/policy nazi on you but I ask that "age" question cause just the way you type presents yourself (I'm not trying to start a flame war but I'm sure a few people will agree here on this) as "hick'ish". Please try and not post repeating/duplicate posts. It just clutters the forum.
Enjoy the day where ever you are.
Glooko
..."In Glock we trust"