You could try doing it the "correct" way by going through the city or something and maybe get a law passed or adjusted, but it's not likely to work, and if it does it's going to take a while. Diplomacy with the neighbors is a good alternative, but in my experience it doesn't help much.
Our family has had to deal with neighborhood dogs causing problems. We had some kill a few of our cats, and that turns my normally very friendly and understanding family into something far less nice. Talking with the neighbors didn't help. An AK-47 to the offending dogs did.
Yep, they called the cops, and the cops basically told us that we did the right thing. The dogs were on our property and destroying it, so we had the right to protect it. Around here at least, the dogs don't even have to be doing anything on your property. If they're there, you can kill them without repercussions. Not that we'd ever do that, of course.
The laws around there might be different, and I'd only suggest it as a last resort, but it's likely to get your neighbors' attention if diplomacy doesn't work. It's also only legal if the dogs are on your property. What you can do when you're out on the streets is a lot more limited, and I'll admit I don't really know.
Keep in mind that people are stupid and irrational though, and if you do end up killing or hurting their dogs in a "legitimate" situation they may still try to retaliate. We're pretty sure one of the guys who lost a dog came by and stole and destroyed some of our stuff in revenge, but at least his freaking dog isn't here killing 14 year old cats anymore. Worth it to me.