Usually when someone has done something bad, they will try to play it off or steer attention away from it. In chapter 41 on page 14, when Chris is at the police station, Mr Boone sternly tells Chris not to investigate. He says, "Christopher, you have to stay out of trouble, OK?" and "Just try to keep your nose out of other people's business." But when Christopher insists that he is going to investigate, Mr. Boone gets angry and says, "Leave it." He also tells him again in chapter 79 on page 32. Obviously he wouldn't want his child going around harassing people, but it's very suspicious when he gets so mad and frantic when he hears that Chris is investigating. In chapter 4 of The Hounds of Baskerville, on page 47, Stapleton tells Watson not to go into the Grimpen Mire. This is because he is hiding something. This would link to Mr. Boone because if he's hiding something, he wouldn't want Chris to investigate either.
In chapter 79, on page 32, Christopher gets in trouble for poking around Mrs. Shears garden. When his father confronts him about it, Chris shares that Mr. Shears is his number one target. He says that he may have wanted to hurt Mrs. Shears, and could have done that by killing Wellington. Mr Shears had motive, but he also had opportunity because he knew Mrs Shears and Wellington and could have easily gone back to the house, gotten a garden fork, and killed the dog. To other readers, this would make more sense because you can argue that Mr. Shears was very comfortable around the dog and Mrs. Shears, and also had a better opportunity. This draws attention away from Mr. Boone as well.
As much as Mr. Shears has a good motive and lots of opportunity, that is just a ploy to focus attention on that instead of the real killer, Mr. Boone. In chapter 67 we learn that Mr. Shears left Mrs. Shears, and that is when she and Mr. Boone became very close. But throughout this whole story, Mr. Boone and Mrs. Shears never interacted once. It's seems weird that there was no explanation as to why they don't talk anymore. Clearly something happened between Mr. Boone and Mrs. Shears, which could have been part of Mr. Boones motive. Also, in chapter 97, on page 39, Mrs. Alexander tells Christopher that his mother and Mr. Shears were having an affair. If Mr. Shears was the one to leave Mrs. Shears, then he wouldn't have motive. Mr. Boone may have wanted to harm Wellington to get at Mr. Shears, because that is his dog as well.
No matter how much Mr. Boone tries to encourage Christopher not to investigate, it is obvious that he is the killer. He has a short temper. He drinks a lot. His job makes him stay up late. Add up all those details and you have a case of a dead dog, an autistic boy, and a secretive father, who also happens to be a killer.