If you don't handload, you are going to find that you can get far better deals on .223 ammo. And also have a much wider variety of loads to choose from. If you mainly just hunt coyotes, though, that will be no concern, as your shooting volume will not be very high. But if you start making regular trips to hunt prairie dogs, then you should consider that.
If you wanted one rifle that is flexible enough for both types of hunting, the CZ 527 Varmint model would be an excellent choice. And it is available in both .204 Ruger and .223 Remington. It is light enough to handle quickly in a coyote hunt, yet its barrel is heavy and stiff enough to provide repeated excellent accuracy too, when shooting volume is high.
Remington used to make a nice lightweight varmint rifle called the 700 LV SS. However, they stupidly dropped it from their product line this year. So CZ sort of has the light varmint rifle to itself now.
Here is a photo of what a CZ 527 Varmint model in .223 Remington looks like:
Here is a link to an excellent review of the CZ 527, if you are not familiar with this rifle:
http://www.gunblast.com/CZ-527.htm
Checkout this group that the reviewer shot with the rifle, just using Remington factory ammo:
That was done with just the standard model 527, and not the 527 Varmint which has a heavier and more stiff barrel.
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