he he he.........I posted this same question on another site recently after watching a Coyote segment on Versus and as I don't care what passes for a delicacy in China, I don't eat dog but it sure looks like fun.
The general consensus I got was shoot em and leave em. You use the first kill to bait the others in and if you got a buyer nearby for the skins or the pelts, then the shipping cost won't be too badbut most don't bother as a lot of em are too mangy to sell unles you skin em.
and here's a tip,farmers hate em and some will even pay you to shoot em.