When I first got my Axis in .223, I ran a bunch of cheaper factory ammo through it at the range to see what I could get. I ran 62 gr. FMJ AE (american eagle), 55 gr. FMJ AE, 52 gr HP (forget what brand it was), 45 gr HP Remington green box, and 45 gr. HP Winchester white box (the crappy tire/walmart 40 pack stuff).
I ran 20 rounds of each in groups of 5 (cleaning between groups). In my gun, the 62 gr. did the worst, the best results were with the 45 gr. HP white box, the remington green box was a close second. Best group, if I recall correctly was about 7/8" at 100 yds. It seems that my particular rifle liked the lighter, faster bullets and hotter loads. Expirementing with handloads for it backed that up. My pet load right now is a 50 gr. VMAX over 22 gr. of IMR 4198 and rem 7 1/2 primers (muzzle velocity is up around the 3200 FPS mark). With my handloads it will shoot 5/8" at 100 depending on how much coffee I've had that morning.
I haven't taken any coyotes with it yet, but did wreak havoc on gophers at dad's last summer, longest shot was just under 300 yds with a cheap tasco varmint scope (6-24x42). I will qualify by saying that I took one ranging shot first and adjusted accordingly (meaning I missed the first time

). Really the only downside of this gun is the factory trigger and the long action gives me some ejection issues (if I don't cycle the bolt hard enough the empty brass will not clear the feed path).
Your mileage may vary, have fun,
Nathan