jvic, let us consider all of the alternatives.
a)Varmit hunters are allowed to continue to shoot them.
This is, of course, a humane way for them to die. Personally I've never hunted varmits with the exception of groundhogs, which were to eat. But it is my understanding that varmits hunters take a great deal of pride in making long range head shots, therefore a quick, painless kill.
b)Poison is used to eradicate them. As SDwhirlwind illustrated this is a less than himane way to dispatch them, or any animal for that matter. (I kill cats that come onto my property but would never consider poisoning one of running over one. That, to me at least, is inhumane.
c)People, not unlike yourself, volunteer to come to the areas where they pose a problem (at their own expense) and trap the varmits, inoculate them to prevent the further spread of disease and rid them of their diseases. You, as one of the volunteers, then flea dip them and (again at your expense) transport them to an area where they pose no threat to the ecosystem of the people and/or livelyhoods of the people living in the area.
In order to do the latter you will first have to be inoculated yourself to protect you from the diseases that they carry, collect the necessary funds to accomplish this overwhelming task and then locate a suitable place to transplant them to.
This, all of this, is (and I think you will agrre) is damned unlikely to happen in our life time. No?
Then we have.......
d)The all knowing powers that be, living in their gated crystal palaces in Washington, knowing far more what is good for those living in areas in which they have never seen, cave into the cries of bleeding heart liberal bunny huggers, not unlike yourself, and pass legislation to protect the varmits. No more hunting. No more poisoning. No more freedom to deal with pest on ones own property. Anyone caught doing so would be declared a bad, bad American and dealt with accordingly.