I've had to change tires before out in the bush while wheeling-without the nice tire jack and proper tools, it's a pain. A long handle, wide bit screwdriver will work, along with a pry bar, but again, it's a pain to get them off. Once you do get the tire/wheel off the machine, you can set the jack itself along the edge of the tire, then proceed to lift the machine with the jack. You won't actually lift the machine, but once there is enough pressure on the jack plate, it will pop the bead. It works well with full sized rigs when necessary, but I don't know if an atv has enough weight to do the job.
A trick to get them on is once you have the tire on the rim, you can wrap a rope or tie-strap around the middle of the tire, then spray some ether inside the tire itself. Light a match, the small "explosion" will cause enough pressure to "seat" the bead-as the rope keeps the tire from expanding down the midline, also may melt a bit of the inside rubber, helping to further seal the tire to the rim. Had to use that ether trick once when a truck was froze solid in a small pond-when we tried driving it out, the wheel broke free, spun freely inside the tire, with the tire still froze in the pond. That ether trick melted it enough, or popped the tire back enough to "seat" it well enough to hold, and get us out.
Probably a more "safe" bet would be to get the tire on the rim, then again use a tie strap or rope to tie it tightly around the midline. From there, use a 12-volt air compressor and pump away, till you hear it "pop" on both sides. From there, back the pressure down to whatever you desire. This will take a lot longer to do, but will work in a pinch if need be.
These little tricks should only be used when necessary in an emergency situation. Basically, if you have the tires, just want to swap, I'd just go down and have the local tire shop do it. They can pop the old tire off, set the new one on and send you on your way for about $10 per tire, in less than 10 minutes. Much easier, much faster, and definately much less of a headache.
Anyway, hope that at least gives you a couple ideas, and best of luck!