First of all, you're not going to stop Air Bud, you can only hope to contain him. He found pay dirt against us five times before we even knew the game had started. This player has a nose for the end zone and probably worst of all he's got easily twice the agility of any defensive player you have on the field (four legs against two, not hard to see the advantage.)
You are going to have to commit at least two defensive backs to the task of covering Air Bud. If you think you can put a corner all alone with this dog and not get scored on all game, then you're fooling yourself. You're going to want your best shut down corner on his case as soon as he crosses the line of scrimmage and then you'll need to put your fastest safety over the top. That's the only way it's going to work.
This brings me to my next point: try pointing out to the refs that the Timberwolves have an actual dog on their team, not a mascot but an actual non-human player. I have a feeling that there's a rule against this somewhere. There has to be. Even if dogs are allowed to play football, this bastard doesn't even wear shoulder pads, which I KNOW is a requirement.
I've talked a great deal about Air Bud's strengths, but realize that he is a player who makes many rookie mistakes. He's exceedingly undisciplined and if you can get a good deal of crowd noise he's liable to commit false start penalties. Also, you could try tossing tennis balls onto the field; those usually get him to jump across the line as well. Most importantly, we have to realize that Air Bud is in this league, he is an offensive weapon, but that doesn't mean we shouldn't try to minimize his impact. If you can force the Timberwolves to spread the ball around to their other (human) receivers, your team might just be able to hang in the game and knock out this high school football juggernaut in the making.