Bluedeacon,
I have never tried the new HEVI shot myself, mostly because I have so much of the old lead shot fodder around here already. /ubbthreads/images/graemlins/smile.gif All I know about the HEVY shot is what I read about it. The HEVY shot is odd looking stuff, not even round. It is harder than lead or steel and from what I read about the stuff, it shoots good patterns even from standard modified choke tubes. It is expensive to buy, but sounds like it may well be worth the price if you are really serious about shotgunning coyotes.
In the lead shot line, you want to use copper or nickle plated shot that is buffered. Federal "premium" or Wincester XX magnum in either BB or #4 BUCK (not birdshot). Like Stu has already stated, the 3" fodder will whack coyotes grave yard dead at 40 yards (or further). For best results you should pattern your gun/ammo through different choke tubes to see what your gun likes best and where the pattern is actually striking in relation to where you are aiming.