Fred Eaglesmith wrote a song called "I Shot Your Dog":

Well, hello, neighbor. I been meaning to talk to you.
I been putting it off. It's something I gotta do.
I been living with a secret. Been keeping me awake.
There's just something I gotta say:

I shot your dog. He was on my property.
I thought he was a coyote, on the run.
I been missing some chickens, so I pulled the trigger.
I feel so bad 'bout what I done.

He also wrote one called "He's A Good Dog" which, although the dog is alive, he predicts his end:

He's a good dog, but one of these days
I'm gonna have to drive him into town and have him put away
'Cause he don't hear that good no more and he can't hardly walk
But until then I'll look at him and say
He's a good dog