Any flat shooting deer rifle with a good scope would be plenty. But do you have the skill to shoot it accurately is the question? A 250 yard shot on a dog sized target is not a gimme, and would require proper sighting in of the rifle with the selected ammo, a good solid rest to get an accurate shot, and care to make sure nothing or no one is downrange. Also if there is more than one, don't expect to kill more than one at a time. At the first shot, the dogs will be in high gear and not very many marksmen can hit a running dog at 200 plus yards. Also, any marginal hit will really be noisy, as in the dog howling like mad, and this will draw the attention of your neighbor if he is within hearing range or if the wounded dog makes it home. I got not problem shooting dogs that are not where they need to be doing things that they shouldn't. I killed 7 out of a pack of 10 a few years ago as they were running deer on my place, and many more over the years. Even have a few bow kills. But I do use judgement when doing this, and understand that it will really piss off the owner, maybe even enough to cause retaliation or even violence against you. A buddy of mine was even arrested for doing this same thing, and it cost him a lot of money in legal fees. So beware, be discreet, and cover your tracks. Discreet is hard when a high powered rifle is discharged, and even more so when a dog howls bloody murder when hit. Believe me, been there, done that! So don't let your anger get you in a bad situation. And if you do decide to shoot them, please practice if you are not a hunter or marksman, of get someone to help. You may also consider other options that would be more discrete, like trapping them. I know a few other lethal options, but I had better not discuss them here on a public forum! People who let their dogs run free to kill game or livestock are despicable, but unfortunately pretty common. Think this through before you act!