You' right about the solar, those are really expensive! But you can run electric fence wire cheaper than you might think. For dogs you don't need a real powerful charger, the cheap Fido-Zap units work fine on them if you put the wire at the right height (so they get zapped on the nose - once is all it takes). You don't put the charger out by the coop, you put it wherever you can plug it in, then run electric wire out to the coop. Aluminum fence wire is cheap, I think less than $20 for 1/4 mile. Bang in some T-posts, get some of the plastic stand-off insulators and run the wire out. You can even run it overhead if you have tall posts, or you can run it through PVC conduit laid on the ground; I have even run it through drip-irrigation tubing, which is super-cheap (use a vacuum to suck a string line through it, then tie the string to the wire to pull it through).
It is kind of a pain and costs maybe $100 or so, but it WILL keep dogs out. If you shoot the dogs, more will just come along eventually. Hot wire will also keep out the raccoons, skunks, foxes, and anything else with a central nervous system, if you set it up right. I can't imagine trying to keep chickens without a hot wire.